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Full text of "Monthly notices of the Royal Astronomical Society"

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THENKW Youk] 

PUBLIC U/JilA 






ASTOB. LSNOX AND 
I TILDfN FOoNDATIo^S 
*»_ 1908 



J 



I N D E X. 



PAOK 

Altitodo, on triirnnometricsl ditTeroncna of, G. T. M<'C*w ...^ 567 

Atiiiiul General Meeting, iqo? Febru»r>' S, report of lli« 8I5 

AhscLi &ii>l prtuwril properljf of ihv Society » S2I 

Ajnociat« «l«!t«(l — .*. 497 

Amooiktc pro|iaH{^(l .,, 365 

Aitrogntpllic cAUli^^nie, od th« noMibilUy of imitroriug the plMcn of 

tlia refereijre eUrs (or, 11. H. Turner 108 

Atitr'^^rsphic chart and citologuc, Connoil noie 00 187 

Au<litorH, rejinrt of thn 390 

Aurora! obiorred at IMtiug, Brae, Shetland, 1905-6, Be?. A. 

Hetiileriion , 105 

B*T7»rd, E E., oathe '• 0*1 " nebola, Mewier 97-S".Q.C. 3587.... 



)U 



■ 543 

Baxendell, J., obwrrniiuus of b' (lamiii'iraiii : «dit<Ml by H. If. Turner 316 

Heiiut-ati to tiie t;i<n<rnil faiiilti of llie SoaJely 2SO 

Uocholfslieini, H. L., ohitanry notice of, aaS 

FViiie. Rev. John, obituary mitii-e of 319 

Browo, K. W.,tlieOoId Mfd>d prorated to him I'm- Ms reiearcbet io 

tln' lunar ihwiry 215, 226, 300 

Caiiilmilgf- Obsarvatory, rspurt of tbe iirMMdingsor , 254 

Candidates proposed I, 107, I7i, 216, 363, 435, 4«r 

CajM o( Gftod till))*, lioy&l ObarrratorTi report of the proctsdings of ... 248 

Celoris, G., tlic medirva] evtiiines of, P. H. Ci)well 17 

Chmtiif, W. K. M., nrto on tbu di<tvriniiiatiou of tlio wire-in terrain for 

_ a trsDnit instrumoot 185 

Cbristir, W. IT. M-, A. S. EiIdinKCon, and C. DaridAOD, on tho tnttn 

of a pliotogra plied i<!-»c«u 175 

Clerks, Agnes Mary, fibitiiary nouoe of 330 

CoinetB :— 

[904 I. (Brooks], observed at the Lirerpool OburratOTy 97 

1905 I. (Encko), observed at tho l.iverp"ol riW-rvitory 99 

1905 II. (KorrelJy), obwrvedat the Liverjjool Observatory 99 

1905 III. (Giacobini), observed at [li>: Liverpool Obcrvattiry 100 

1905 IV. (KoplI), obtatred at the Liverpool Observatory ., loo 

1905 V. (Soliaer), obwrvwl at the LiTcr^HMit Obsrrvstot* .. 100 

1906 I., observationi rrom photographs, Koyal Obeervat 
wicb 

o 1906, obierratiotis from pbotographi, RojnU Obae' 

wich , ., 

b 1906, obaemtioDi from photographs^ Boyal C 

wiob - ..,, 

d 1906, observations from [ihotographs, Boya 

u-icb 

« 1906, olnervationi from photographs, R« 

wioh 

9 1906, nbserfalioDs fniin pbot^giaplis, 
wieh 



- - -" 






tLOM 

Halley'K, uou- on tJi« ai'|>rDHc1iiQt< retuia of, A. C. I>, Cromniflin.. 137 
HallBjr'a, ibo psTturbfttiona of, V. H. CokoU not] A. C. D. Crom- 

jneliii 174, 3S6, 511 

Oa the flffwU of radistioo un tli« luotinD of (iwrojid uotc). 'i^. C. 

riumm«r 63 

Cuniela of 1906, Cotiuoil note on 373 

0^'0^c^ W. K., the rliiotrio arrangementa of an olwerTstory .. 421 

Oouksoii. ]i., iini) II. F. XcwmII, note on the spoctnim cf a Omnii 482 

CoriiB, Rvv. A. L., iiotii an the riKUal s|iei'tium of Wit*. Cvti iu 

l}t)C«inl>er 1906 537 

rOMtneil, repcirt of ttie, to the S7ih Annti«l General Meeting 217 

well, 1*. H., the mMiicva] eclipHK of Cvloria 17 

— HkDat«eii'e eclipM tc Stlk]«stftd. 1030 Aiigntt jr 136 

— on th« Jiipitcr cvection tvrin 356 

ancient •■cUpset « 508 

Cowvll, P. H.. nn(] A, C. 0. Oromnialin, the perlnrbatioilB nf Hdley'ii 

comet ...174. 3^*6. 511 

Cromnielin, A. C. D., note on the .-ip^n-nai-hing returii of Ilallcy's ooniet 137 

— the (vrojier iiKition of Caator 1 40 

Appendix t*> Ubt, A. WiliUms' obserratjoni of 

ocfiultslioiis 361 

Croninieliu, A. C. 1) , and P. H, Cowetl, ihr [terturbfttiona of Ualloy's 

coniel 174, 386, 511 

Dallnwycr. T. R.. nhitnary notice of 331 

Daviithon, C, W. H. M. Cliruti<i, uiil A. S. Kddington, erron of n 

{ihotognpht-d t^Heaii ..... . 175 

Dt-uniug, W. F., early aoU iiite I'erHids 410 

— nnie on a nictmr ttliowvr (th« Auf^iat Dracontds] 5*^ 

Donner. Anderi, elected an a«ociat« 407 

Downing, A. M. W., the phii-dt of xndiiical etarii for the ejKM^ 1900. 186 

not«on L« Verri*r's tablei* of Satarn 4J6 

■ - Qon)i>arisnnM nf the pliieco of Wars caloulated frnm 
KewccMnb'a t^ibles, with the places (-jiicul&t«l from he Vt'rrier'* 

lablob. nuar lb» times of ap^iositiun in 1907 and 1909 575 

Dunaink Observatory, report of tlia procat-diDgi of 257 

Earth's azia of rotatioQ, tha irregalar moTt^ment of, J. Larmor and 

E. H. Hin« as 

Sddington, A. H., the srotamitic moLlona of the itan 34 

Eddington, A. S., W. H. M. ChriaUe, and C. DarldftoD, erron of • 

photographed riSieaa 175 

EdltibnrgD Uoyal ObMrratory, the latitude of thr ...'...... zia 

— ■ ■ niwrt of the proceeding* of 353 

Rrrata 364, 496. 5/6, 577 

B«|iin, Hev, T. E., microinetrical rncasom ordi)iibt«atars(iourtb s«rio»] 190 

new dooblo stars 194, 495 

report of bin ubflorviitary 262 

a new nebula 360 



ETeridiad, J., dislrihutioii of protiiinencvs in latilnde tti the yrar 1906, 
from obMrvatious made at Kodnikiinal on 1(6 days in the flrtt 
half of the yeer and 105 daja in thr neoonil half 477 



FeUowa eleotod 1, 107, 173, 215, 315, 365, 497 

Finncmoro, K. I., oMtoair notice of 231 

Fowler, A., enhanoad tiuoa of iron in the rvgion P to 154 

nolo i>n silicon in the obroiiiospbere 15? 

the origlL of cortuin bands in the spectra of mn-apote 530 

Pranks, W. S,, nutit on t!t« coluura of a and (Mtra) Csti $3^ 

the relation betwarn star eolonni nnd spectr* 539 

Frepotan, J. H.. obituary notice of 23a 



Ul 



Geodesy, Cguudl unle on ago 

Gil), Sir D., and S. S. HoukI>. di.'t«riit)ii>Tions of iMieoDa) iKitutioii 
(leinimliiig on uiigiiitade, mwle with the tmnait circles uid Iha 

helioinet«r it the Koyn] Obaerratory. (^|'« ol Hand 1\q]<* 366 

CSIufiaw ObAcrvattiry, report of the |>rocet'ili)ig» of 257 

{lUduill, Jouph, otntuary nntice of 25* 

Oold Mi'dal, tD«, prtisentod to ProfeaHor E. \V. Browu for bis reararclies 

in thp lunar thsory 215, 226, 300 

Qrkdiiated oirck, ucidMital produvtiQii of temwinr? errors of divUioo 

on a, W. M. WilcIiBlI 149 

OieeDuricli Royal ObM-rvatorjr, nbaervations ol the aatcllite of Negitane 
from photographs taken b«tween 1905 DvcomLar 19 and 1906 

April 25 91 

obiorration* of oonift c £905 from pholo- 



gnj>ba takeu with th« 30<iDch reflector of tlio Thitm|«u» iijiia- 

tonal 

alMieivuUon.s of i-unmta 1906 fiom pltoto- 



94 



gr.ipbH takt-'ii vrtili the jo-iui-h retlcitor ol the ThumpGon ei|U«> 

toria] 95 

obeervationa of cotni?t£ 1906 Irom photo- 



graphs taken witb the 3oiiich ratliictar of tb« TliotnpUD equa- 
torial 

obnerratiaua of minor phuicta front (ihoio- ' 



96 



gru)h« tikcu wiih the jo inch rcllectur of the Tbotnps.>ii wiun- 

tonal iluriug the jvara 1903-5 151, 202, 336 

mean an-ni and htrlio;i(rBphio latitudes of 



■UQ-epota in tlia year 1905, dniticcd from photographs tnktv at 
Onteiivich, iit Ilehra Di'in, tit Kridaikanal ObaerTatorj, India, 

and in AlatiritiiiJi . i<^ 

ubservtttiou3 <if oixultutioua uf ataia bj 



the 3[oon made in the year 1906 209 

' leport (if ib'B proi-eMlings of 343 

o» tbe ritliio ot thr solar [^triUax reanlt- 



ing from th« Orei'Dwioh pbotograpba tif Ema, 1900-1901 3S0 

observatious of Jupit'r's lixtti and 

sevunth aatolHtes from photpgrai'ha lakrii with tbe 3<m'iio1i 

ntQcetor ill 1906-7 479 

ohmrvatioiifi of coDiett (/, » and if 1906, 



from photographs taken with tho jo-IdcIi rcUeclor of th« 

Thonipsuo oquatonal 511 

diai^rams ahowttig the [H<mtioi» of 

Jupiler'a MlrUItm VI and V[I, from pbot-'grapha tukvn 
dtiring tho (tpiKuitioiia of 1903-6 and 19U6-7 561 

Hagen, J. 0. , jpttvr lo Profeaior Turner on the oom|nnaon atan for U 

(jatnlnomm 330 

Heatli, T. R., doscription of an M{aatortaI mflecUng toleacope drivcu by 

a hydraulic ram 527 

Hfllwiln ObsbTvatory, desrrtptloii of the 30-ilieh p' < . 

J. H. Heyiiolds .. (47 

Handeraon, Hev. A., auroiw oUm-itkI in tl. 

Shetland, from Se|.taiiiber lyuS tf - 
HHU, M^or E. 11., a»<l J. l«niior, the u.^:^.. . 

Karth'a axis of rotation : a anotribiilliin u v >. 

itacaueH 

Rinka, A. R., Holar [mraltax |<«i' 1 

graphic niacin of sLiit j. 
Rinka, A. ti., and H. N. Rnaaell, Ibt 

grap ha token at the CambitiJi. 
nough, S. S., and Sir D "■" ' ' 

dei-ending on m n 

betiouieUir at the L lj 



iv Index. 



^ 



^ 



PAflB 

Hu|q:iiiB, Sir \V. , rei»ort of lii* obwrwlory 363 

IniMA, R. T. A., conipdiftiioR ofMcDUr permrUiions 427 

• '— — — — i^mta 576 

— — table* Tor the appUoution of Ur InueR'i metliod, 

F. RoM.iiis 444 

Iron. eohanuHi Hues of. Id the ivgioD P to 0, A, Fowter 154 

Johrijiton, WilliBin, obitti»ry o otic* of 233 

Ja[)it«r«vection Urm, on tlie, P. n. Cowt-ll 356 

obaenrfttiuuB of, during th« ap))«rit{oo of 1906-7, Bar. T. B. R. 

Pliillil'ii saa 

Jupiter's BaU'U;t«8 V*I nud VII, Coiiiici] notcoii 373 

— -— — — ■ — al«er<ratiaiui froiu pliotognphii ukm 

At the Koyal Ob*en'tttory, Giecnwiclt, 1906-7 479 

(liaffranm Ahawing the [lottlioiui of, 

Ibotn plinlogrsphs lak«u at Ute Hoyal Obaervatoi^, UresDwioli, 

1905-6 aiid 1906-7 561 

Ki^pler'i eqaatioQ, uot« on a ni«ch:iuical M>lut!oo of, II. C. Plunimcr. ... 67 
Uoaaikaiial Obterralotr, distril)Utiuu i>f [^ruiuim^uces iu latitude in the 

year 1906, J. Evarsbed 477 

KodaiUnal aiia Hadna Obaorratories, report of thv iiroc^tadiiigi of 264 

Lauglay, S. P., obituary iictice of 239 

LariDDT, J., and SUjor E. H. Hills, the irregular movi'mt^nt of tha 
EHrlh's axia of rotniion : a c»iitributi>iii towAnJt the aiialym 

of itacauMi 33 

Latitudir, tho, uf the Knyal Otiservatoiy, Ediiiliurch 3i3 

Lb Varrier'iubkaof Sitnrn, noteoD, .\. M. W. Downinf; 436 

Lvwio, T., noti) Ui ftaxcnilKira obaerrationa ofU G«iiiiiioruiii., 331 

Lewlii, T., and H. H. Turner, on the tncliuation of iHuarj- atar orbita to 

thaOnlaxy 498 

Library, etc, of the Socioty, list of dooora to the „ 394 

Liverpool Obwrvatory, cometary obsenratjona, 1904-6 97 

report of the pn>cc«dings of. 358 

Lout, J., ou the present of tin in stellar atmosplierw 487 

HvOsw, 0. T., on triKonoiuotnoal diRierctircs of altitiidff $67 

Man, oompariaons of the placrit of, ciilculated from NawcornVa tablea 
with thrix! from Le Vt-rriRt's talili'S, ut-nr itie tinie» of opiiaxi- 

tion in 1907 and 1909, A. M. W. Duwnitig 575 

Maunder, A, S>. D., an appnroot influence of the earth on the iiuinbars 

ami ireaaof 8iiii-»p«)tsin tht cycle 1889-1001 451 

Maw, Vi*. II., nililrc-vi on pr«Mnting thf> Qold Medal to I^rofemor Emeat 

W. Brown for UiH fHearcbea in the lunar theory 300 

' Udbourne ObaerraCory, niport of tbfl proceediiiKi of .. 36a 

Melbounie and Sv'incy Olworrstoriea, joint report un ttio niMHurvmont 

of ftfltrogrBphicplutea 363 

HerJield, C.J., licti' mi i nation of tho secular [irrtiirbationaof ibt minoi 
planet Cerea, arii^ing from the actions of Ui« eiglit tu^or 

plaiietd of chc Molar system 551 

Matters : — 

Council note on the progress (if meteoric aatronomy in I906 275 

Early and late I'eraeid^, W. F. Denning. 416 

Measurement ot a meteor trail nn a [>ht>tu^rai>h>c plate, H. K. Turner 563 

The AagOBt Draconida, note on the, W. F. DunninR 566 

Minor planet Oen, accular perturbations uf the, C. J. Mer^elil $$l 

Minor plnnetA, oliecrralions trom photographs taken iu 1903-5 at tha 

Royal OhacrvBtory, Greenwiob 151, 302, 356 

Council note on the diaoorery of. 1906 369 



Index. 



nam 

Mnnn eoIipsM : 

Tlie oArly foliiwvti uT tiia Sud and Aloon, E. Nwill 3 

Aiioluiii iM:Ii|>8ftit, P. H. Oowoll 508 

Moon, cK>oulUtion uf Saturn by the, i9o6 0oti^)er 27, J, Tebbult 197 

Uoou, occtiliauoni of -tan by tbn, 1906, ot>Mrv«<) At Uic Iloy«l 

ObwrvatAry, Oreflnwirli . 209 

observed by IUt. L. A. WUIi&dia 361 

NebuU. a uew, Eev. T. E. Espia /. 36a 

the "Owl/ (M 97), E. E. Barnard 543 

crrtU 577 

K«]>ti)i)v, tlie satellite of. lOMi-rvationa from photographti lakou ai tho 

Royal Obsurratory, Grei-Dwicb, 1905-6 91 

Nrvill, E.. tlio caily oclifnnn of tbi" Sim nii<l Moon 3 

y«w&|j, H. I'., iioUii oti some tt{wctrosco|>k- obarrvatiaiis of tlitSiin 158 

NvwaII, H. p., ind B, Otiok^ti, note on thi^ H|>iH!truD) of a Oriouii 482 

2f«mll tclMCfii>c. Oiiibrjd^ Obserratory, re|>ort of ths work of 256 

NIcholla, A. E., obituary notiiiH of 133 

Obituary Koltow : AasociatM :— 

Langlcy, Samncl Pifrruont 239 

Oademaiii, Jeaii AUnibam Clirvtian i ...» .,, 241 

Obituary Notices: Fellows: — 

BbcbulTslicim, Baph*«l Louia „ aaA 

lloiir, John as9 

DallmeyaT, Thomas Kudol^liiu .t ajl 

Fionemon'. Ualicrt I.-H:tac „. „ »....n SJl 

Kreeniaii, Jo»c[>L U ...,. 933 

Gledhill, Joaei>li , sja 

JulinittoD. William .'. 233 

Niibdlla. Alfn-i! Edward „ 233 

RawBou, UoWrt ."....„.... 334 

IteyiioU*. William John «,..,« m6 

Scwtlt. Phiiip KdwnrI Ijfi 

HimuB, William ...,„ 237 

V«D:ib1i«, Ucor^e ; „ 238 

OUUinry Notip«; Ilmiorary Memlier:^ 

AgON Mary Gierke .„, 230 

ObMrvatorini, n-iKtrtii of itrocaniirifca of ."; 243 

Obverratorv, electrio arraufit'iiicDU of an, W. E. Cooke 421 

Offioeraani) Council, 1907-8, liat of. „,. 314 

Oudrmaiifi, J. A. C. obituary notico of 341 

Oxford, it&dL-liirf> Obeenratory, laport of the procMJiogs of 258 

— raagiiitndr o( « Cell {Hin}, igo6 

December 14 — 1907 Fobninry 16 412 

Oxford Univurvity Obnorvatory, ro|Mirt of thu [irDceodings of ,. 360 

Paria Etoa Circutar, photographie plaoM of statu in tbo, A. K. Hinks ... 70 

Prak, Sir W., report ofbia ob«irrvatory 

Pirsonal Maatioti dapendinK on ma^-nitudv, datanni nation :> 

Gill and 3. a. Hoojjh 

Perth Olifiei-vatorv, Weeteni AuNiialin, rc[ 
Pbilliiw, Ui-T. T.'E. IL,obw)rTatioQ>orJ»i< 

1906-7 . "".. 

PholoKraiiha, reti^tiai, lint of reprodnotioiia of , 
Platw :— 

Irrrirnlar moTenieBt of the hUtrtii^i axir 

£. 11. HilU 

^iiit-h phatografitiic reflector, J. IL li 
Tho " Owl" nebula, E. E. Itariinnl. 
PoattioDf of Jupiter's aaulUtaa '^' : 
GnicDwtcb . 



Index. 

lumiiier, 11. C, on llio olivets of raiHatiou on titr tiiotioni or conuU 

[Second Note) 63 

not« Oil n iiu-ehaiiiAnl Boliitiaii of Ki^tilerN 4"|u«tioi) ...... ^L 

I, N. It, obmrraiious orU Gemiuonini, frlit^ hj H. H. Turnar 11 
en^itniii 



Prwcnts auiigancwt 1, 107, 173, 315, 366, 425, 4^ 

ProgrusH KuJ preseut HUte of tho SuoJdty, 1907 2I 

Publication* of the Sooiety 



Rawiion, Kulwrt, obituary notice of 2j 

lUlli-iilor, [ihoLPiirR]iliic, i>f the Holwan Obscrvatorf, description of the, 

J. E. RB.yiioId* 

- 0(|ii(ili)riu1, ilrivet) by ra liydr&ulii: ratii, T. E. Heslh 53 

u. emu of a \)\iotogtii\ihcd, W. H. U. Cliriatie, A. S. Eddinfitoii, 

ami (;. DnTidoili IJ(j 

nolJs J, U., d&icripuon uf tbe jo-incli {fhotogntpldc rotlector of Uit 

HelwAn Ob&«rvitnry 

BeVQoldi, W, J,, obituary notice of. 

Ronbins, F., tables for ihe aiiplication of Mr. InoM't mttliod of 00m- 

putiiig Bt'cuLir inTtiirlwtioBB 

Rnberti, A. W., report of his obscrvfttory 

Riij(liy, Ti'iiiple obserTatory, ruport of th« iiroceediiif;9 of 

*11, U. N., Stellar panlUit papurs, No. 31 the parallux of tiiglit 

»tani, from p)iolo^r«{)b)i wtvn *i tho Ouibndgo Obserratory 

by A. R. Hlaksand ibo writer i; 



itawiK 
^neynt 






Saturn, oocultation of, by ths Moon, 1906 Ociobsr 27, obwrvad hj i, 
Tebbutt „ 

Council note oil tb«n«w aatellitMof ; 

—— note uii Lc Vi'rriiir'«» tubliw of, A. M. W. Dotrntiig 

Snuiniiir, S. A., report of h;a ob>en-ati>ry 

i^-ciiUr iH-rturliatiaiit-, the coiiijiutation of, It. T. A. Iiinpji.. 

arrata J76 

tables for the application of Mr. Innea's method, 

F. Hobbini , 444 

oftJie miuorplaiiAt Certfl, G. J. Merfield J51 



3«'«ell, P. E., obituary notice of 236 

Ijidgnavt'H, Rev. W.. tlie spectium of Mira Ctli in Dvcembor 1906, aa 

I'liutograpkodat Stonyhnrst Obxtrvatory 534 

SimiiiB, William, oliitiiary noticu of 237 

Sontli Koiiain>,ton, Koyal Co)tcf;r of Scieuci.', report of th« prooeodtUKS of 262 

' Solar Pliyaics ObMrvatory, rei>oit uf the |irocv«Klingi 

of 261 

S[B'ClroMrtprji. rvnolvtn;: power of, E. T. Whit taker 88 

Spflclruui, coittiiiuiHiH, dUtributiou uf niiier^ in tie, E. T. Whitiaker... 85 
Star Ciitalogupj* : — 

Aincrican Kphemeris Catalogue of lodiacsl stars for 1900 and 1920. 

Council not« on 28S 

Cape tifueral Calalogns for t90u, Couni'il nuLo aa 28£ 

flvnderson's Oatalofriio for 1840, Council note on 289 

Ambroun'HCatalogaaof allataratu Sf'S t^r 1900*0, Council noU) on 289 
Gap* CaUtloguc of aatrograpbic standoixi stara for I90o'o, Couuoil 

nolo on 289 

Antronomlacfaa GeMllacliaft OftUlogua, Council Dot« oa 290 

St»ni, Donbla : — 

MUTotntirioftl meaMurw of double »taT« (fonrtli aeries), Kev. T. E. 

E»pin , 190 

NdV double star*, Rev. T. £. Espin 194, 495 

Council nnt« on z8o 

On the inclination of binary star orbits to the Galaxy, T. LsiriB and 

If. n. Turner 498 






I 



I 



Iitdex. vii 

YhQt 

^kll»x of:— 

ilWruJlax oreisht sUr», frora pbotof[n>pha talci-ti at the Cmnliridgt 

Ohs'Tvatoiy by A. R. ITiiikaaiKl n, N. RuKi>«)l 13a 

SUra, pboto;^a(ihia placeH oX, iu tliu Paris Kn>N Circulnr, A. E. Hink*... 70 
StATi, propLT imiljooB of :— 

The propar motion of Cft^tor, A. C. D, Cninimulin 140 

Batimato of th« nuinbrr of tMn iriUun cartain liiniti of proper 

luotiuii, W, CI. Thackeray... I44 

Propor mutiun* ilnriveH rruin a cani|>ari9M>n nf CarringtonV CaUlq^tfl 

witli the Greenwich jilacc-s for 191X), W. U, Tliackeniy 14(1 

Stars, rrfuirnce, for Ui« Asti^raphic rjihilognit, 011 tlm pouibilily of * 

improving the plaoei of tlw, H. H. Tumor 108 

Stan, «i>m'tri» of:— -' 

Council note on Stollftr spwlroacnpy tn 1906 ..■. 283 

Notv on the spftctrum of o Ononis, IL F. Ntwall ami B. Oookaon,.. 4il2 

On the pro««iicr of tin in nUlInr atitiuBphero. J. Ltiiit. 487 

The reUtiou betwcti trtar cok>un( au<J M)ei-tra, W. &, Frank* 539 

Stan, BVBletnttlii! nuitiuiiN of the, A. S. KiMiDfttoi) 34 

SUrs, Variablu :— 

Caiinoil ijote on zKa 

On the ulnssification of lonK-nertoil variaMe iitsrn, and k poasible 

physical iiitarpr«t»t)on, 11. H. Tum<>r 332 

Note on the ratigc to bri^'htm-ss at iiiuxiniom of lonff-period 

Tariable§, 11. H. Tumor 489 

U Ueniinoruto, Po^onN obHorvationk of, ciiilcd by H. H. Turner... 119 

arrnt uni 496 

Bnsen<l<-ll's ulwrrvatiotin of, «lit4>ij by H. H. Turner 316 

» (Mlra) C«li, mapiitude of, 1906-7, obMrvt^ at the KatlclilTe 

Ob«'rvat«ry, Oxford 41Z 

(Mira] C«u, Hpectrxim of, 1906 Dcccmbsr, photoxnp^od at Stony- 

hunt, Rov. W. SidgrvMveH 534 

■ ■ — vihiul Bpectrani of, 1906 Decembsr, Rev. A. L. Corti« ... 537 

(Mim) and a Oeti, notv on the colnurs of, W. S. Franks 530 

KV Andraiuedte, elements of, A. S. Williums », 491 

RX Aii(lroin<Hlic, A. S. Williaiiis 493 

R, zodiaral, the nlacw of. for tbo «i>och 1900, A. M. W. Dowitiuff ... iw 

_^ny hurst College Obsarvatorv, roNirt of the nn>c«eiJjng9 <o\ 362 

Snn, chrotnoflpban, note on nlicon id tbe, A. rowler 15; 

Sun eclipsea : — 

The early edIpMi of the Sun nnii Moon, E. X«rUl a 

Tlic inetfin-rM eclipMK ofOlorin, V. H. Cowoll ., if 

Uauat««n'a e«lipM at Stikl&auid, 1030 Aiiguat 31, P. II. Cowell 136 

Aiirieiit «clii*i», P. H. OtWi-lI... 50S 

Sua, i«ralUx of tbc, on tbe valne of, rmiUing Inm tbfl UrMnwkb 

photographa of Eroe, I9cx}-I90t *, 380 

San prominencea, 1906, CoouiTil not« on 979 

distiibution o(, in latitodo in tlia year 1906, from 

oliservations at Ko<lnikiuiii1, J. m1 477 

Siin, Bpcctrum of the : — 

Knhanci'il lines of iron in tli* A. Fowler 154 

Not«a on sotim •p(H-trr«<:Qpic ' hf Sun, H. F. Nc'Wiill 158 
San-ipota nnd fniMilii-, el«:. : — 

ilaan areu and bitiofcmp ^.;, from photograjiba 

taken • h, Is 19S 

CoBn«:iI m. .'-Vkti 278 

An ai (i areas of 

^ ■ 45< 

Ttaf ■ i hun •spots, 

A ' ..■■■ 530 

Sydney 01-. r, lo^ 

Sydney and Maj> snninuiii 

ofaittiogn- \ij' 



Tiii Indax. 

nam 

Telilnitt, J., aliMmtioD of th« oemiltctinn of S«tuiii hj thf> Hood, 1906 

Oototiw 27 I9f 

repurl nf his otuwriniiory 3S8 

Thacker&j-, W. (i. , ritimate of tli« minib«r of itUn KifMn crrtun Itmiu 

of [iriipPi motion.., 144 

notes on some proper motions ilr-rived from n oom- 

pftrison of Cumngton's CatJilogue with the (rn-«tiw)ch pluc«i for 

1900 146 

Transit in si ramptit, determination of wire-interTih for, W. H. M. 

CIiriHtio 1^ 

Trrimuri-r's an-oTiiit for :go6 2lS 

Tniat ftaiida aai 

Turner, H. H.. on the possiliility of improviiig tlie pWei of tlie refer- 
ence sttn for the Astrographk Catalogue from the iiliotf^rapliio 

taeasam ., loS' 

Pogson's obiorr^tioM of U Geminomm 119. 

— — — - BrratTiin 496 

— Baii'iidoir»Q)i!)ervatiori!4 of U Cienituonim 316 

on the claAaifiaitiiin of Imuf^-periail variuiilu stuns and a 

possible physical ititerpretatiun 33a 

note on tlie i-atign in brightne.u or lonit-iwriod variaMce 489 

— on Uie mHunretnent of a ntet^nr trail on a photvfrrapMc 

put* 56a 

Turner, H. H.. and T. Lewi*, on the inclination of binary star orbita to 

tlip Owlaiy - - 498 

UniTPmal time. Counril iioteon 290 

Veoablca, Itev. (leorjie, obituary noticA of 238 

Wbittaker, E. T., on the JietiibuCton of eangy En thf> oonrinuous 

apcirtnim 85 

on the rwiolvinff j>oW(ir of tpiotio«copeB SS 

Williams, A. .Stanley, elemental of tltd vnrtii.Mi' »tar RV Artdixnuoiir ... 491 

on the variable star RX AO'lromedfl! 493 

WillianiH. Bav. L. A., oSservAiions of oi-cnltatiaii& 361 

Wilmin, W. E., rBjwrt of bin olwervntory , 364 

Witnliell, W. M., on ihp iwtjiiii'nial produolion of temporary errora of 

ilirigioii on a gratloatcd circle 149 



H 



MONTHLY NOTICES 



OF THR 



ROYAL ASTRONOMICAL SOCIETY. 



I Vol. LXVIL 



NovE&iBKR 9, igo6. 



No. I 



I 



W. H. Maw, E«q., Phistdent, in the Chair. 

Ralph Falcon, M.A. Oxon., Camerton Hall, Workiugton, 

Cumberland ; and 
Arthur Grant Stillkamer, Yerkes Obaerviitor;, WilUums Bay, 

Wiecouiiiii, U.S.A., 

were ballot&l for and doly elected Fellows of the Society. 

The following candiUatos were i^ropoeed for election m Feibwa 
of the Society, the names of the proposers from personal knowledge 
being appended : — 

Rodney Boyce, Soudan Survey Department, c/o the Royal 

Colonial lustJtute, Northumberland Avenue, S.W. (projjosed 

by K. P. Cotton) ; 
Arthur Cletninsun, Deputy Commissiouer of Landi^, Lagoe, 

We«t Africa (proposed by E. P. Cotton) ; 
Qeor(;« Inne-i, M.l'.S., Cbemittt and Optician, Olive Bank, 

Edinburgh {proiwwed by Rev. Jnlm Spencc); 
Arthur Kent Lucke, Suez Canal OjmtiHiiy's Sfrvite, Tran'«iL 

l>epartment, Isniallia, Egypt (proposed by E, W. Maimder) ; 

and 
George Street. M.A., Tutor, Merton House, Soofhwirk. Sassez 

(propn«ed by Arthur R. Hinkn). 



I 



One hundred and aixky-five presents ■■ 
been received since tbe laat raeoiing, iwz- 

Galileo, Opere, Ediziu NttfOMlAi vob. il 
by the lUdian Govemni- ^ - ' * ; ', 

■chaft, Abtlieihing ii. ^ 
■ented by Professor Betk 
Attronomincfie Oeteii/fh-ii. 
Appliol Optics, preaeutel 






Mr ^evill. The Ewrly Kclipses of 




LXVII. I, 



Seventy'eigbt clmrte or the jVstrographic Chiirt of the Heavene^ 
preaeated by tko Koyal Observatory, Grecuwich ; and iuuety-«u 
charts, preseTit«*d by tlie I'aris Observatory. 

Two enlitrged traiiapareni^ies and latiti-rn slide from negatives 
af the total eclifue uf August 1905, taken »t Alealft Chisvort, Spain, 
pr^aeuted by Ctmnt de la B.iuruu Pluviiiei. 



Tha EaAy KcXipten of tht Sun and Moon. Ry K, Nevill. 

With the view of furnishing Mr Cowell with th'- further 
information he desires (Mmxthhj iXofirfs, vol. Ixvi. p. 474), I huve 
<>xtractecl from tny memoir on the <.)bflerved F.rrorfl of llDnsen's 
Tables de la lune tuy iavedtigation of the naults yielded hy the 
obcKrvatiuiiB of Ihu aucieiiC Eclipses of the Mooii contained in 
Ptolemy's Aitnayest. 

'J'he fcMppee nnd Hrrorit of Hannon'R Table^t are 115 follow : — 



r 


' IM*. 




ri«c«. 


PtuM. 


Brror d( 

QftHMIt'l 

Tablea. 


M'elghl. 


R«jii&rla. 


i . 


- 710 M»rcL 


"9 


Babylon 


Begiuutiig 


33"' 


2 


Toul 


3 


- 719 Hareh 


8 


II 


Middle 


-63 


i 


Hag. =0*3$ ou 


I: 


-7i9Sepi. 


t 


.. 


Ue^DDinK 


-43 


2 


Mag. =055 oa 


- 620 April 


21 





Bn;;i lining 


44 


3 


Ma^, =0*25 on 


5 


- 523 July 


:6 


., 


IVgintiiiitf 


93 


I 


Mag. -o'soon 


« 


- 501 No?. 


19 


1. 


lk)(iniiing 


-28 


1 


Mt«. = 0*35 on 


7 


- 490 Apfil 


25 


II 


HiiRinning 


-2» 


1 


Mag. -0-17 oa 


8 


-381 Dae 


22 


AtbeiiH 


Bi^^aaing 


-51 


i 


SmaLl. Hitca ni 


" 9* 


- 381 Jane 


tU 


Babylon 


Bi^fcioning 


-43 


3 


Partial 


» 




■ 1 


&ud 


-77 


t 


Duration 3*'0W 


to 


-381 Dm. 


13 


»■ 


BepiiiDtng 


59 


1 


ToUl 


It 


- 200 Sejit. 


32 


» 


Beginning 


-z& 


1 


Partiil 


1 IS 


>> 




)• 


Eik) 


-J<» 


3 


Duration 3^ a*" 


la 


- 199 Unrch 


•9 


Alaxaodna 


IteftinniDjt 


-38 


3 


Totnl 


'3 


199 Sepl. 


II 


II 


Hnfiidning 


-as 


2 


Total 


13a 


■ ■ 




II 


Middle 


-19 


1 




>4 


- I7j Afril 


30 


4' 


Bcgiiiuiuf; 


44 


1 


Majt -0*5800 : 


14a 






.. 


£Dd 


-46 


1 


Duration a^ 43n 


»5 


- 143 J*n- 


27 


Uhoa«a 


UcgiuutDg 


-83 


i 


Mag. =: 0-25 ou 


16 


+ i»s May 


5 


AUxaodrU. 


Baginning 


26 


2 


Mag. =0-17 OB J 


17 


f 1 33 May 


6 


It 


Miiidli^ 


-30 


3 


Total 


i& 


+ l34 0eU 


20 


II 


MtiUUe 


- '3 


2 


Mug. =0-83 on '. 


19 


+ 136 Maich 


5 


» 


Middle 


-48 


2 


Mag. -0*50 on ] 


^ 


^^ 


_ 


^^ 


^^ 


^_ 


^ 


^^^ 



Nov. 1906. 



Ute Sun attd Moon, 



The data have l>»cn taken, primarily, from Profeioor NeweomVaj 
Re*MrrAe> on the Afotinn '■/ thf Moon, hnt id certain casM I hai 
ioterpret«d the record in a somewhat different nmuiier^ on the 
Btreogth of additional infomiatiuu, and have a^isumed that the 
Eclipse No. 8 was '>lvi6r%'Fd at AtJtenti, the actual place of observatioo 
bcitig loft uoHpeciHed. Tliitt Kolipse No. 8 atid Kvlipse No. ic ob- 
•cifved At Hbodefl stand id a different category to the otheri, 
•eeiningly having been selected from outside Ptolemy's usual autbnri- 
tiet for 0ornu special reason, possibly because no ocllpsos observed 
at either Itabyloo or Alexandria were observed under the de&ired 
conditions. Neither has b^t^n iiaed in the discuasioti which followa. 

Writing— 

(Tabular — Obeerred) longitude = A L + sin a . A. + cos a . A^ 
+ «injff.B, + C08/8. B, + (T-i8oo).3o''.W» + (T-i8oo)«i".oA 

where a deuote» lh(> Moon'6 mean aiioniaty nnd fi denotes the Mtion's 
mean ar^gument of latitude. Then the preci^Ung data loatl tn the 
expressions-^ 



tlx 



1> 



AL=-^lt*t 


+-SSA 


■*- '47 A, 


- 01 H. 


-•99H, 


* 4*20ir 


- 10*58 A 


= +285 


+ *ii 


-•98 


-•'s 


•99 


+ 4'M> 


- »o-57 


= -'^ii 


+ •33 


-^4 


+ •13 


+ •99 


+ 4*20 


- «o-57 


= - 199 


■31 


+ ■95 


-■:8 


+ •98 


+ 4'03 


976 


= +427 


-^"45 


+ •89 


+ •15 


-•99 


+ 3-87 


- s^ 


= ^^12 6 


^ 06 


^ "99 


-•14 


+ ■99 


+ 384 


- 8-Ss 


» + >47 


+ •99 


-•0T 


- '20 


+ •98 


+ 382 


- 8-75 


= +»87 


-78 


•62 


+ ■20 


-■98 


+ 3*5 


- 7*95 


= + 189 


'•43 


^•91 


■'S 


+ •99 


+ 3-64 


- 793 


= f 33-8 


-'42 


r-91 


-'"5 


+ •99 


+ 3*4 


- 7'*3 


= +35-0 


- Yll 


•99 


+ •07 


"99 


+ 3*4 


7^3 


= ■♦ 12-4 


■82 


+ ■57 


- •!! 


-* '99 


+ 334 


- 6*6 


= + »4-3 


-■S2 


+ •57 


- •!! 


+ •99 


+ 334 


- 6*6 


= *»'3 


* -97 


■22 


- ta 


■99 


+ 3*33 


- 6*5 


- i '3'5 


•96 


•29 


+ ■00 


+ •99 


+ 333 


- 6-65 


= - IO-2 


•96 


■29 


+ "00 


+ •99 


+ 3*33 


- 6*s 


= t35'8 


^-•33 


■95 


+ •13 


+ W 


+ 3-29 


- «'49j 


=s+a7*o 


+ ■33 


- 95 


+ -13 


+ •99 


*3'*9 


- 6-49^ 


= +4«-9 


+ 05 


■09 


-15 


•99 


+ 3*4 


- 6*27 


* + l3*9 


9S 


■29 


-17 


-■98 


+ 2 83 


- 4*8 


= + J4*< 


-■69 


• 72 


+ -08 


•99 


+ 3-81 


- 4*3 


-+6-3 


+ •86 


+ •50 


+ -OS 


+ •99 


+ 2 -Si 


- 463 


= +ai7 


+ ■63 


-78 


+ •19 


■98 


< 2-80 


- 4;&L. 



Ufc— 



A denote the vaJuev ohtitinad from Huiten'a Tftblea, v(\l\i \x\% 



Mr KevUl, The Early Eclipses of 



LXVII. I, 



• 



tabular mean ipotiuiis tuiJ secular acceleratiuns replaced hy Haa- 
BOD'e finaUy deduced values for theee elemeuts. 

B denote tbi"* valuc^a ohtanied frnm llansen'H Tabled after 
replacing his tabular raluea for the secular flecB[eration« by those 
derived tbepreiitally from the secmlar diminution of llie eccen- 
tricity of t!ie terrestrial orbit, reinoviiif,' bis empirical Venus term of 
toDg period, aod making the neceaeary corrections lo the mean 
motions requisite to briug the amended Tablen at> fur a« possible 
into accord with the modem nbservations. 

C denote the values rbt;iined frcim Hanfien's Tablaa after 
applying! the corrcctioua indicated by the «liscufl»ion of the obaerva- 
tions of the Moocr inaile between 1650 aui.1 iSqo, cmploviiiK for the 
Rccnlar acceleration of the mean longitude the value + 7""43, of the 
longitude of the node the value 6"'o7, and of the loogiiudu of the 
lunar perigee the value - 33"*53. 

Then the preceding exprt-ssions yield for the tabular errors of 
the Tables as modified in B nnd L" thp vnhu-s 





Oftte. 




Titlilc* B.— OtM. 


T*blwC.-OtM, 

J- 


iro. 


AL 


A E, N.P.I). 


AL 


AB.N.P.D. 


I 


-720 Mu.n;h 


19 


-381 




17-8 


.! 


3 


-719 March 


8 


- I9'2 


+ 1-2 


+ 3-9 


+ 1-9 


3 


- 719 Sapt. 


I 


-289 


+ 1*8 


-i6-3 


+ 1*1 


4 


-630 A(>ril 


21 


-24*5 


4. 6-0 


- 4» 


+ 5-6 


5 


- 52a July 


16 


+ 2-6 


-24 


J. 21 "2 


-1-8 


6 


- 501 Xov, 


>9 


-26-3 


+ 4-2 


~ 7-6 


+ 3-6 


7 


- 490 ^pril 


as 


-26-2 


+ 5-4 


-iiS 


+ 48 


S 


- 382 Deo. 


as 


- 9'5' 




+ 1-5 t 


... 


9 


- 381 June 


18 


-104 


+ 8-3 


+ 59 


+ 7-8 


10 


-381 Dec. 


12 


- 3'9 




+ 5-8 


... 


II 


- 300 Sept. 


21 


-16-2 


+ 2-0 


- 3*3 


+ 1-6 


ta 


■ 199 IKuvh 


19 


- IO*0 


... 


1 o'5 


... 


t3 


- 199 Sppt. 


n 


18*0 


... 


- 77 


... 


H 


- 173 Ajiril 


30 


4*' 


+ S-6 


- 4^ 


+ 1-8 


15 


- 140 Jw. 


37 


+ 19-41 


- ll 


+a7'3» 


-o'8 


16 


■r-:25 April 


S 


- 6-0 


+ 2*3 


- 0-9 


+ 3-a 


17 


+ 135 Slfty 


6 


- 4-9 




+ 4'a 


... 


18 


+ 134 Oct. 


20 


12-8 


+ 1*4 


- 4'a 


+ 1-7 


19 


+ 136 March 


5 


"*■ 1*5 


-5-0 


+ 7*5 


-47 



The Eclipse No. 8, whose placo of observation ]» not stated, bat 
has been asKumed to be Athenti, yit-lds values fairly acoordaitt with 
tliose from the other eclipses. The Eclipse Ko, 15 obsierved at 
Rhodes is quite discordant, indicating pither that Zech was correct 
in supposing the lirae to be an hour in error, or elso that the phase 
observed was the luiddle of the ocli|Jse : the Rrst supposition would', 




Nov. 1906. 



tfu Sttn and Moon. 



reader the error in longitude 11= - 14' '3 C« - 6''3, and the second 
the values B= - ia''4 C= - 4''5 ; reaults in fair accord with tho«e 
froQi Ibo other i^clipses. Neither eclipse has beon includexl in the 
investigation of the errors in lonijitude, however, owing to the in- 
herent uncertainty. 

From the precoding, there are derived the following values for 
the mean outDtaii'iliQg errors of the Tables b» amended : — 



Epiidi. 


TiblM B.-OIM. 


taIiIm a-ob*. 1 


«r«i«ii 


^H 


Ah 


= -28-7 


=.-'5-« 


3 


^1 




- -24-5 


-. - 4-2 


3 


^H 




--^6-6 


= + 0-6 


2 


K- ~3»t 




>- 8*8 


= + 59 


4 


1 -19a 




= -117 


= - 1-3 


10 


1 -.^5 




-- 6-3 


■*+ 0-9 


2 


+ '34 


aL 


* - 5*3 

= ' ia-8 


= + a*6 


6 


Weighted nianu 


= - 0-9 





U U obvious, therefore, that the^e eclipfiea cannot be reeouciled 
vfith the theiir«tica[ value of the secular accoleratiun in mean longi- 
tude enibndi^-d in 'j'ulileti It, t>r witli any value lenfi than that 
adopted in Tnblea C, nr below + 7''*40. 

Couhidcrin;; the currecliun AB' U> the secular acceleratiuo of 
the lunar node, the mean of the results from the observed phases 
3, 9a, I la, and 14 yield the expression — 



+ 070 aB" -3-62J/' +7'9i A 



TtlilM B.-Obi>. TahlMC.-Olw. 
- - ij'ia = -o"25 

whilat the mean of the results from the obsf-Tvcd phases 4, 5, 6, 7, 
8, 9, II, 14a, and 16 gives 

+ i'384B" f 3'59W' - yvS.'i = - 14*20 = +O'03. 
Henre 

aB'-o'03W* + om3A = -o"*49 = +0"*il. 

The correction obtained is small. 

The values oi the corrections to the tabular K.N.P.D. regordlug 
thera all as of equal weight yicKl the values— 

Kpaeb. Olw. Olw. VfefM 

-565 Tsbtra B. aK.N.P.I).= +3''50 Ts))Im C. AE.y.P.D = +* 
- 172 = +085 = -*■ 

+ 132 =-0*27 

Regarding ihex as indicating a |i 
they Rorrespoud to the value* — 



k 



T«U1«« Ik aE.K.P.D.= +oio 
T*bl«0. *-a-03 



6 \fr NevUl, The Sarly Bdipset of lxvil i, 

These vftluet are too largo to be real, correapoadiog to a change 
of Bome ao' per century, — an iiupoesible amoDDt if assumed to 
extend up to the present time. 

If tliey be rtij^anleil as due to the effect of correctioDg required 
by the adopted tabular value of tlie argument of latitude ft 
necessitated by an erroneous tabular value of the secular utxeleni- 
tion of the Mood's node, thoii the values indicated are — 



Ob>. 



UU. 



Ubi. 



ObL 



-565 Tabl«.B. /, Aj3= -3-84 -3'84 Tftblw C. A AA = J'a3 - 3*21 
-17a -1-45 -3*47 =-iX)5 -a-l9 

+ 132 -277 -170 =-3*07 -»'SI 

oorrespondiDg to the corrections to the secular acceleration of the 
node of 

TablM B. AB= - i'zi {T - iSooy 
Tables C. aB= -377(T- 1800)' 

The' discordance betvdeu the observed and calculated raluea ii 
very great, no that such a enrrectioii can have do real weight. 
Nor can it be iuipruved by any cbango in the tabular mean niotkm 
of the node. 

Taking the vahiea as they stand, they would appear to involve 
an inei(uality in the complete expression fur the Moon's latitude with 
a cuctTicient of about a niiiiuti; o£ arc and a period of from seven td 
eight hundred ycara. Such a term would undoubtedly reconcile 
those values of Aj(j, an<i render con>>iHtent the vahiofi found above 
for the correction to the secular acceleration of the node. Hut it 
could not be rendered consistent with the modern olisurvations, for< 
it would mean a change in the Moon's latitude of iit leattt ten 
twelve eecoads of arc within the period iSzo and 1890; though in] 
all probability the cbani^e would bo at least two or tbn-e times ail 
great, as it is very unlikely that the epoch of the temi should b«1 
such as to render tb^ amuunt of change a miiumum. 

Such a change of the Moon's latitude is quite iucousiittent with 
the ubBerrations. 

Tite Arabian Edijf»eB. 

The Arabian eclipKes r^uoted by Profesjtor Kowcomb in § 5 of 
his liasearrhee "h thn Motion of the Moon, from Cauasin's edition of 
"le Livre ^U In ;iraride Table HakL-milH," have to be taken int 
account to obtain further inforniaiion on the points whicb ha^ 
been dlscutwcd in the previous investigation nf the Ptolemaic 
oclipees of the Moon. 

Professor Newcomb points out that some of the observed 
altitudes of the Moon are impossible, ami some of the obaervad| 
altitudes of the clm-k stars are irreconcilable with each olh* 
Mr Knobol, in Monthly Notice*, vol. xxxix. pp. 338-340^ 
fTDggesta that these impossible values are due Ui errors in copyit 



Nov. 190G. 



the Sun and Moon, 



the Atmbian figaraa, which uften differ so Aligbtly that errors can 
eauly be auule. I have hud no meaus of referriog to the orijfiiiai 
authuritios, but an the result of aunie iniiuJrtes Diode for me by Mr 
Marth, I think that the altitude of Arcturus on 925 April 11, 
which iti given uk 1 1 *, should Ik read aji 31*; that the altitude of 
Aiclanis on 929 Januaiy 37, which \» given as 18*, should be 33* : 
and that tht- altitude of the Moon on 983 March 1, which is given 
a« 66*, should be 62*. 

When the maguitude of the ecJipAeo in givtm, it docti not state 
whether they wore eatimated from the tipper or lower limb, as is 
done by PtoK-my, so that when the ecUj)i*e Is large it is uncertain 
whether the central line uf eclipse passod north or south of the 
centre of the Sun. This renders the interpretation of the solar 
ediptiea of 993 Augtut 19 and 1004 Jaouary 24 somewhat un- 
certain; and though in each case the most pnjbabiu [tath ban been 
taken, some doubt must attach to the results. 

The resuIiA of the inveatigation of theae early eolipses observed 
by the Arabian astronomers are as follows : — 
T^e Early Arabian Eclipses :— 



Eclipses of the Sun obser\'ed at liagdad :~ 

Datv nwac. TftlKlUr liTon. Wdfht. 



MagBltndc. 



K«>iukrkl. 



f 



8x9 Nov. 29 

933 Nov. I a 
9»8Aug. 17 



Bei{iiiiifn>; 
Had 
End 
Kod 



-45-9 
-1810 
-167 
-wo 



KAJeoted, 



5 

3 
4 



Eclipses of the Sun otisArved at Cairo : — 

977 I>«e. 12 Beginning' - 4*5 1 
.. End - 3*2 I 

978 JpDr K Beglnniog - 19*7 t 

., Eud - 3'5 2 

979 Hay 38 Beginning - 6*3 2 
985 July ao Be^finuing -34 '3 1 

„ End ' 147 4 

993 Ang. 19 Beginning - 0-3 2 

.. End - 19'9 I 

1004 Jan. 24 Scanning -il'i I 



025 

074 

o-«a 



Eclipees of the Moon ob^nred at Bagdad : — 
854 A ag. II Bc^uniDg - 7'i t 

Ss6JttQ« 31 Beginning - 37 2 

9^3 JuD« I Rnd ~ 67 2 

925 April 1 1 BpgioDing - 4*5 1 



Knd 



+ aa 



8 Mr Amtf, The Early Eclipses of 


Lxni. ■ 


Eclipaeii of the Moou observed at Bagdad — continued. 


1 


Kij. Dftto. Ptiaso. 1'abulkr Brron. 


Wiighk 


MftgnltDilc. 4I 


5 917 S«pt 13 B«gianing 


+ I3'a 





Doubtrtl. Tims poMibly caki 


6 QI9 JaD. 27 BrKinniiif; 


-17-8 


1 


Altitiida oorrected for err*r ias 


7 933 Not. 4 Ilnginriiiig 


i'8 


2 




J 


Eclipees of the Moon observed at Cairo : — 




1 


8 979 Hiy 14 End 


H-3 


i 


DoubtJ'ul. pDrhaps etlcuUtod 


9 979 Nov. 6 Be^inaing 


- 3-4 


I 




1 


9« ., End 


- 13-9 


I 




-i 


10 980 Ahy 3 End 


- 4-8 


1 




■ 


II 98iApril2i Begitming 


3-8 


1 


AltgDitude =o'23. ^^H 


lift ,1 iind 


^ 1-6 


I 




^H 


13 981 Oct. 15 Ba^nntDg 


- I4'8 


1 


MaKo'^ds =a'43. ^^H 


13 9S3 Mtrelt 1 Retiming 


- 49 


I 


Altitude eorrocted Tor •rro^^n 


I3« „ Eml 


->7V 


z 




J 


14 9&6 Dec. iS KegLtining 


-192 


a 


Magnitu<I«< =0'83. fl 


15 looa M&rcli 1 BflginnLug 


- 3*S 


2 


Ti>t*l. 


^m 


From tbosu oliservutions 


are obtain 


id ihe following exprciwions : — ^ 


Eclipsea of the Sud : — 










I a1.= + 7*6 +'98A« 


+ -|6Ac 


- -06 B* + *99 Bt 


+9701; • - 


S = + 67 - -90 


+ *43 


- -10 


+ ■99 


+876 


3 =+4-5 -'99 


+ -14 


■•-•05 


+ •99 


+873 


4 =+17 -19 


-•98 


- '11 


+ •99 


-I-8-42 


4A =+ l-l -19 


-^ 


- Ml 


+ •99 


+ 8-42 


5 = + S'4 -'^ 


+ •96 


+ TDI 


-199 


+8-41 


5« = . I '9 -26 


+ •96 


f -OI 


-■99 


+ 8-4I 


6 =+ 3'8 -90 


+ •43 


•13 


-•99 


-!-8'40 


^^L7 = + 10-6 4- -99 
B7A =+ 9*1 +-99 


-•14 


•09 


+ •99 


+ 8-15 


-•14 


•09 


+ •99 


+ 8-15 


S = + o-| + '44 


-■90 


-^04 


-■99 


+ 8-06 


8* =■■¥ 10-3 + *44 


-■90 


-•04 


•99 


+ S-06 


9 =+ 4'4 -'94 


-'33 


-•05 


-•99 


+7*96 


EcUpiei of tlie Moon: — 










I aL=+ 36 --66 


-76 


- -or 


-•99 


+ 945 


3 =+ 1-9 +"99 


+ •00 


+ •» 


-•98 


+ 9 43 


3 =+ 34 -'39 


■i -92 


fl4 


+ '99 


+ S77 


4 = - 3-3 +•93 


-•38 


--09 


+ •99 


+«7S 


4" =+ I'l +93 


-•38 


-•09 


+ ■99 


+ 875 




^^^^^^H 


^^^H 


^^^^^^^H 


^^^^^^^^^^H 



Nov. 1906. the Sun and Moon. 

Eclipses of the Moon — continufed 



= + 


9-1 


•90 


-■44 


-■ 


10 


+ 


.99 


+ 871 




-1.26 


= + 


09 


■57 


+ •82 


+ ■ 


'02 


+ 


•99 


+ 8-64 




-I 25 


= + 


17 


•96 


-•27 


+ • 


II 


- 


•99 


+ 8-20 




- I'I2 


= + 


7-0 


■96 


-27 


+ ■ 


11 


- 


■99 


+ 8^20 




- I'I2 


= + 


2-4 + 


■80 


+ •60 


+ ' 


■06 


+ 


'99 


+ 8-20 




- I-II 


= + 


1*4 + 


•07 


+ ■99 


+ ■ 


02 


- 


•99 


+ 8^i9 




- Ill 


= - 


0-8 + 


■07 


+ •99 


+ ■ 


02 


- 


■99 


+ 8-19 




- I^Il 


= + 


77 + 


•37 


-•92 


- 


•16 


- 


•99 


+ 8-I8 




- I'll 


= + 


2-5 


•85 


-•53 


-■ 


09 


+ 


•99 


+ 8*17 




- I'lO 


= + 


8-9 - 


•85 


-53 


-■ 


•09 


+ 


■99 


+ 8*17 




- I -10 


= + 


97 + 


•17 


+ ■98 


-■ 


'10 


+ 


•99 


+ 8*15 




- i-io 


= + 


i"3 


•07 


-■99 


+ 


•06 


- 


■99 


+ 7-98 




-106 


From these there 


are derived the 


followiug values : — 












Tablei B.— Obt. 


i 


Tabtea C— Obi. 

* 


Weight. 






AL. AK.N.P.D. 


kL. AE.N.P.D. 


AL. AE.N.P.D. 


Eclipses of the Sun :- 


- 
















1 


829 Not. 


29 


^i-S 


( 




+ 5'i 


' 


I 


... 




2 


923 Not. 


to 


+ 3-8 






+ 6^0 




I 






3 


928 Aug. 


17 


+ 1-7 






+ 3'9 




2 






4 


977 Dec 


12 


-1*4 


+ 2-4 




+ -8 


+ 2-3 


2 


I 




5 


978 June 


8 


- -8 


+ 4-5 




+ 1-3 


+ 4-6 


4 


1 




6 


979 May 


28 


+ i"l 


... 




+ 3"3 




2 






7 


985 July 


30 


+ 7'4 


+ 2-2 




+ 9'4 


+ 2-1 


I 


2 




8 


993 Aug. 


19 


+ i*o 


-41* 




+ 3'o 


-4-0" 


3 


I 




9 


1004 Jan, 24 
no (weighted) 


+ 2-0 


+ 2"9* 




+ 3"9 

+ 3"2I 


+ 2-8' 


I 


t 




Ha 


+ I "CI 


+ 1-68 


+ 165 




Eclipses of the Moon 


: — 
















I 


854 AUR. 


II 


-09 


... 




+ 1*3 




I 






2 


856 June 


2! 


-2-4 






-0'2 




2 






3 


923 June 


I 


+ 0-5 






+ 2-8 




2 






4 


925 April 


II 


-27 


+ 3*i 




-o'5 


+ 3-0 


4 


I 




6 


929 Jan. 


27 


+ 6^2 






+ 8-4 




I 






7 


933 Nov. 


4 


-1-9 






+ o'3 




I 






9 


979 Nov. 


6 


+ 18 


+ 2-7 




+ 39 


+ 2-8 


2 


I 




10 


980 May 


2 


+ o'o 






+ 2'0 




I 






II 


981 Ajiril 


21 


- 2! 


-0-6 




+ o^o 


-o^7 


2 


2 




12 


981 Oct. 


15 


+ 5-2 


+ 1-2 




+ 7-2 


+ i'3 


I 


1 




13 


983 March i 


+4-3 


+ 6^2 




+ 6^3 


+ 6-1 


3 


I 




M 


986 Dec. 


18 


+ 7*3 


- I'2 




+ 9-3 


-'•3 


2 


1 




'5 


1002 March I 
kti (weighted) 


- 1^2 






+ o'8 
+ 273 




2 
1 






Uei 


-hi 15 


+ '■34 


+ i'5C 





to 



Mr Nemll, The EaHtf Eclipses uf 



LXVU. I. 



The mcuti rcnultu being the iiume for botb Kolar aad Iniikr 
eclipxe«, they may he UDited into one aeries and yield tlie valaee — 



pocJi. 


l^bld B.— 
Obt. 


TbWw c— 
Oba. 


WslghL 


Tatitet B.— Ota. 


-nbiM a— 

Ofai. 


Wd0 


849 


aL = -075 


= +150 


4 


&a?r.p.u= 






937 


= +0*11 


= 4.225 


[0 


=:+3'IO 


= +3X» 


1 


98] 


= -ri7g 


= -*-rS8 


ao 


= +a*ii 


= *ix>7 


10 


999 


= + i-aa 


= +244 


6 


a - 1*65 


= -1-65 


• 



Umd (*olRht«<l)= + t -23 = +3'>» 



36 



= + '•45 



1-41 



Thoiie Arabian eclijmes yield insults in accord with thetheorp,ticaI 
values ol the secular HCRflleralion^ anii admit of being properly 
rt*].>i-«HO[ited by nu vahiL' of tbe secular acceleraUon iu mean, longi- 
tade greater than M 

+ 6"*ao 1 

whereas it ha» beeu shown that the Ptolemaic ecltpeos of the Moon 
can be represented by no value less than 

+7" -40 

Ucticc Iwth KcrloH cannot bo properly rcpreaunted by aay one value 

of the HeciUar iicce I oration, as t]ie mean value 

+6" -So 
faila to represent eitbor. 

CoQsldering the tabular erron in B.N.P.D., there are mvi 
eclipses by which the error can bo determined through the obaerv* 
duration of the eclipsir. Th'-se are — 



Hotar Ecltpw*. 

977 Dw. 12 
97S July 8 
985 July 20 



TabiM B -Dili. 
B.N.P.D. A A* 

+ 2-4 -2-4 

+ 4-5 +4-5 

+ 2*2 -2'2 



tunar Ec1lp*«». 

925 April 1 1 
979 Nov. 6 
9S1 April 2t 

983 Mftrnli I 



TaltiM a.— Ota. 
EN.P.D, A ail 

+ 27 +2*71 

+05 -0-5J 

+ 6-3 -6* 



+ 3*03 -0M3 



+ J-J2 -17J 



The errors regarded ua errors in E.N.P.D. are the same f[ 
both solar and lunar eclipses, bat regarded as due to erroi 
In the adopted longitude of the node, they are disoordaut. 
united, they yield the menn values — 



AE.N,P.n.= +3*-o9 



Afl= - ['-03 



Hence, like the Ptolemaic eclipses of the Moon, thoy indicate 
uoifonn correction to the tahutar E.N.F.D. rather than the need 
a correction to the tabular longitnde of the node. 



Nov. 1906. 



th* Sun and Moon. 



II 



The six i»lipsei where the recorded mugnttude U available for 
determming the tabulitr terror in K.N. P.I). art> — 



SoUrKcUjwM. 

985 July 20 
993 Au«. 19 
1004, Ju). 24 



T&bl«t S.— Oba. 
&C.H.F.U. A A0 



Lutuw £cllpan. 

981 April 21 
981 OcL 15 
986 Dec tS 



T>I'1«E a— ObB. 



AE.S.P.D. A AB 



Meat) 



+033 -I-I3 



- 0*60 + I '40 



If theee be united they yield the raean values — 



AE.N.P.n. - -o'-i3 



Afi - +o''I3 



But the Bei>arato results arc rinite discordant, and disagree with 
the results nbtained from the observed durationtu A fl3f(itcmatic 
difliareiice between the rexuEtM obtained from the magnitude and 
duratiiiu of nii eclipse is quite posaiblo in tbe caso of the^o early 
obeervatioud with unassisted vision, en|H;aal]y in the caae of a 
lunar eclipse, bat the observatious do not indicate any difference 
i>f sensible extent. Thus, in the ease of the aolar eclipse of 985 
July zo, tlie observed duration and magnitude yield thu vaioe 
value for the error in E.N.P.D. In the *.'aHe of the lunar eclipse 
of - 173 April 30 the observed duration ia 2'"4 {jreater than that 
corresponding to the obiit'rved niagnitudt.', whiUt in the caite of tbe 
lunar eclipae of 981 April 2i the observed duration is 4'"*5 lesa 
tbau thill indicated by tbe ma^itiide. 

[f tbe two serioe bo combiuud thoy yield the values 





Tkbhi U. -Ofa«. 


T&bl* B.-f)lM. 


Weig 


Solar Eclipses 


AK.N.P.D= + r68 


A Afl = -o-58 


6 


Lunar Eclipnpfi 


= +i'S3 


= - 0*41 


7 


Uoaa 


AE.N.P.a= + i-6o 


,>, Afl = - 0-49 


13 



From the preceding investigationa the mean value* for tbe 
errora in E.N.P.D. for tbe different epf>cbs may be written as 



S6S 


AE.N.P.D. 


= +3-50 


,', A« = • 3-84 


- 17a 




= t^o-Bs 


= -»'45 


♦ |J» 




= -0'«7 




+ 980 




= + i"6o 




-ftSoo 




= -00 





It is obvious that no correction to the 
nor to the mean motion and secular aeceli 
will serve to repre^ient theM values, thonp 
bring tliem into closer ac 
with H coetlicieuc of ab 
hundred years. 



N.P.D. 
node 

e to 
•od 



12 



Mr NeoiU, T)u Earhf Eclipses of 



LXVli. I. 



Disre^iirdLQf; the apparently [toi-iodical variatioas, the observed 
Taliiea are best repreecnttHl t>y tht: expreAsioii 

T^r Afl = -o"-5o(T- i8oo)-o"-33(T- 1800)' 

but the weight of such a cprrectioit must be very email — to he, in 
fact, n mere pnsaibility. 

By aasRtning that Lh** obeerved tabular error U due to a gradual 
change in both KN.P. D. aiu) argument of latitude ^, a clomr 
agreeiueob may be obtaiuud. SeparatiuK the obaervations into thow 
uiado at lhi> twu nndeH, the results tire 

.lovndtftfr A'ddf. Dttcetulittff Sod*. 

-6k) aE.N,P.D.= -d'-6o we^ht a -540 aK.N.P.D.= -t-s'l* weights 
- 2 = - yio 2 - 31 

+987 =+i'44 5 +978 

Himb may be raganled us indicating 

Ob*. 



= * I -76 
= +1-70 



Oto. 



Oftl. 



-580 AE.N.P.D. = +22; AAB = -2-87 -a-4i 

- 17 = -0-67 - -1*43 - 146 
+ 983 1 + 1-57 = -o''3 o'20 

corrwponding to the com^ctiun 

i^rAjS = +i"'oo(T- iSoo)-o"-3oCT-lSooy 

but it la obvious that the reftult^ for thti middle epoch are liie- 
oordant, 

It 1)1 to ho remembered that the ubnervatiouH t(i thu three xroups 
were made under sumvwhat diffennt ccnditioue. The firsi group 
consiats of itb^i^rvationA made by Rabjiohian nstronnmers without 
the aid of any ij)i<tnimenlal njeane ; the second group by Oreciaii 
asti'onnni'nrK nrith Romr inf<tnnnenti)l aid ; and the third ^roup by 
Arabian astronumerH by Lhe aid of pinule ^Taduated atttrolabee. 
It is pussilile, therefore, that the estiumtw uf ma^niLudee may ba^l 
syfttoriiatically diffcrunt ; and it in iiotewnrthy that if it be Biippo«od^| 
that the (irenian nst.roiiomerA nnderestJimatwl the raannitiide of the 
five ec]ip»t:a i>b;Herired Iwtwceii ~ 20Daiid + 136 by a digit tut taken 
from the aouthoni limt», it would change the observed errors of tb' 
luiddlo groui> lo 

- 3 aE.N.P.D.=:-i'-26 -31 4K.N.P.D.= +3'-38 
corro8[K>nding to thp derived correction 

- 17 aE.N.I'.1). ^ + I'-Ol T*i 8A ^ +2'*47 

thas reducing thu dii^re)ianoy, but still leaving it far too tarjre foe{ 
any contidcnc:e to be placed in the resulting value for the corroctiun 
to the node. 



How far (iothe results obtained in the proceding investigatiutit] 
of the obaervatione of tbeeo eatly eclipees agree with Mr CoweiraJ 
coDcluiion that the ^ftMn's ar^'ument of latitude ehows a seculi 



Nov. 1906. 



the Sun and Moon. 



13 



acceleration about four and 11 half secondtt greater tlian thai tbeureti- 
cally iudicutcd by the sucular dvcrctttiu io tlic vcceiiCrieity o( tbc 
terrestriul orbit I 

[t wiU bi) fteei] that tha contact obeervationft of the Ptolemaic 
pctipseH do not iodicale tbe existence of auch n correction, and the 
similar ob«:rvattuiis of tbo Arabian eclipctvn do not extend over a 
sufiiciently Ion;; period to enable aiij conclusion to bo formed. 

Tha observed iiia^iiitiiili:s of tbu»e Ptoletuaic eclipsei", however, 
may be re^Tirded ae indlcuting the existence of a NCciiUr term of this 
nature, tbough of Mtnaller dimenfiioiin ; but thf> dtnluc^etl correction is 
entitled to little weight, as thn aeparnte r«;sult8 are far from accordant 
unless a eoiisidumble term of Umi; period is asaiiiued to exist, aod, 
as they etand. seem more cunaistent with « secular cliango iu the 
E.N.IM). of the Moon. 

The magnitude and duration of tbe early oclipaes of the Sun and 
Mood olwerved by the Arabian tmtrononiei-s, likewise, indicate the 
existence of a correction to the tabular E.N.P.D. of the Moon, which 
miybt be ascribed to a secular term in the expresision for the Moon's 
argument of latitude of similar character to that suggested by Mr 
Cowell ; but the separate results show discorlances greater than can 
be ascribed to outstanding errors of obKervatiou, whicli renders it 
difticuit to say whether whnt is indicated is a change in the adopted 
secular variation in the argument of latitude, or an analogous chango 
in the E-N.P.D.'s tlieniatlvej*. 

Wijen the two series of ecli|WB observations are luiited, unfurtu- 
nately it becomes -still less easy to reach n d"-^fiuite conclusiou as to 
which cause the ob«erve>l d^ viatiotis fntnt ihtr tabiiliir K.N. I*. D. are due 
to. TheoliBerfeddiBcordances are so considerable, whateTBriiiterpreta- 
tiuti Ihj given, that little wei^dit can l^eHsstgned to the conclusion which 
is drawn. Still, though the wtright niity be xmnll, tin; observations 
can be held to support the existence of a secular terra in the Moon's 
ar^uaieut of latitude greater than can be deduced by theory from 
the observed decrease in the eccentricity of tbo terrestrial orbit. 
Tat they are ali«o consistent, thoujih in a lesser degree, with a secu- 
lar increase in the observed E.N.P.I>., and in this connectiim it is to 
bo roiuoiiibi'red thstTycbo Bniln-''s.'b!U!rvatlons indiait^an K.N.P.D. 
greater by 40" than that twsigned by Jlansen's Tables, and that 
the eclipi'es of the Sun during the period 1620-1670 indicate an 
E-N.P.U. from 10" to 15" greater than that assigned by the table*:. 

The only conclusion that can be legitintiitely drawn from these 
early ecli|>Hii obnervatinn.s appears to be ):hat they are certainly not 
inconsistent with Mr Cowell's concltisiou that the M nent 

of latitude requires an increased secular acceleratioi 

III my memoir it vhx decided tlmt the uncvrtui u 

tbe correction to the tubular E.N.P.D. indicated e 

observations was toa great for them to be taken i 

determining Uie correction to the tabular value of 
the lunar node. 

A'atat Otacrvaloty ■ 
iga6 August 17. 



H 



Mr Nffvill, On. the 
On ih< Earltf EcHptet. By E NeviU. 




The following notes will serve to elucidate some points in 
Cowell's paper on the AncimU EcHpte* in Monthly Noticeit, vol. bti 

P- 473-. 

Aa it was Dot propoaed to aav. tbceo records of early eclipses of 

the Sun for deriving corrections to the lunar tables, but oaly to 

ascertain how far they were represented by the amended tabloH, it 

waa judged sufficieitt to employ Approximative fonna of caluulation ; 

and the data for thin purpune were obtained during my viait to 

England in i8go, from Oppolzer's Canon der FiiuUmitigf (Wien, 

1887), by upplytug to hia data the correctiona Decesanr}' lo reduce 

them to the theoretical valiieft of the secular acceleration in meui 

longitude, longitude of perigee, and longitude of node. 

Tbe elemcnta employed by Oppolzer are stated to corre8{Hjn«i to 

the following ; — 

!•• It .4 

o^jo-26*34T - 3"574T' - o-ocx496(l 
O'oo-26'J4T- i6*a73T'- o'oi684iT 
- S'SO + 53'o6T- 2*956T"-otJ04jjiT 

where T deuotes centuries reckoned from the epoch 1800. 

To reduce these bo the tbRoretical values of the aeealar accelera- 

tioua, it is ueceasary to apply the corrciction^ 



Mean longitude - - 2 •496'!* 

Lmigitmiir of Perig*o^ + i^'izST' 
Longitude of Nod» -+ a-672T* 



I 



At the Maine liiut-, in order Co bring the amended tahloj^ iuto 
accord with modern observal iona, it i» necessary to apply the further 
correctiojis 

Mt-an longituild = - 30*ooT 

LongttDile of Perigee = + io"SoT 
Longitude of Ned* = + s'ooT 

Hence the total corrections to he applied to the elements of tl 
Moon'a orbit employed by Op[]oIzer in order to reduce them to tl 
theoretical vulues are ; 

aC=+ooo- 366T- 2-4967* 
AA = +o-oo + 3714T+i3i2ST* 
4ll=+o-oo-4S-o6T+ 2-672T' 

OppolzerV formtilm for calculating the latitude ^ and longitude 
of tbe potition of the curve of central totAlity for the beginDini 
middle, and end of an ectipae are 



Beginniiig aiii * - - coa t'eoa (N' -f- W) 

Uiddle Bin(*-»')= "in W coiec N" 

End rin = + coa a'eoi (N* - W) 



is' 

*= -M+ ^co«W-Un(N'+W)( 

'5' 



ootN'einW 



«»W-Un(!f'- W)< 



Nov. 1906. 



Early Eclipses. 



»5 



where 



sill (*■ - w ) 
toD A = taa • . ooa L' 



ft ~ i$'.H ' *-^. nnVf . oot(N'+A)-Equ«ti{mof Hme. 



Here 



H donotM the e]wch of coijanctioii meunrvd fh)tn Ortenviftb Noon. 
h, V (l«nots tiie Intit itdc of tlio Muon uid fluu. 
«, t' (trnole th« horixanUil panlluxc!* of tlio Moon kaU Sun. 
L', ft' d«Dnta llin tnia ImigitiiidiH an<i derliiiatiDD of thn SuD. 
4 deootcB tli« olditiuity of tiifl Ecliptic. 

The (ither qiianfcitieR nra taken as they dtanil from Oppolzer'e 
Carton. 

It is nbrious that it ta oiily W nad ft. that will suffer any 
matoriat cliange by tho introductioo of the correction A£, AA, aod 
AB. 

Tlieu a daiiotiuK the Moon's mean anomaly and fi the Moon's 
argament of latitude, 

whftTo approximate)] y 

AB B - cos jB{(0'092 - O'oo6 cos a}&B + 0-0074^) 

cofi(ir+4)| 



and 



where approxinialely 

4^= - (zy-fis - i-38cos«)AC+»'"64*'<'*"- aA + o'-35aB 

The changed path of the curvu of centrBl totality can be doducod 
from ttic coaipari»i.ia of the new pDsitton» of the livginaing, middle, 
and the end of eclipse with tboae given by Oppolzer. 

For the required purpose thiii approximation wan MifHciently 
accurate. 

It wiiK iu ihn (utiuu inaiinur thttt the approximatu piitbs of the 
ditt'erent ectipacfl were calculated on Mr (JowreLl's original data. In 
the uaae of the ecliiwe of - 1 1 16 Jnne 18 an accidental error in 
copying out the final correction oh plus instead of minus led to an 
inaccurate result, and thi^ •^cHiwh cannot have been that observed 
at Babylon. 

I cannot concur with Mr Cowell's method of bringing - 1061 
July 3 1 within the month of /Sivin. The intercalary moDth? 
never iuMrted at the beginning of the year, and the fintt uf 
could not have been later than the early part of April, ao 
laonth of Sivan must have ended in the be{ ' 
luteiit. Nur L-iin I cimcur with Mr M 
tlioagh July 3i8t could not )iuve fallen 
the known Habylonian calendnr, yet i 
a&^umod that, as the epoch is prior to 
calendar may be supposed to be quite • 



i6 



Mr Nevill, Oti the Early Sdipses. 



Lxvn. 



be used after that era. If audi urbitnry iissutnptiuus have to 
made, thn reconls of the.'^ ecHpaea are absoltitely valuelctefi. 

On Ibis qnestion I would nbfterve, merely, that it miiet not 
forgotten tbal tor many centuries prior to the epoch of this eciifW 
the Bkibyluutaus bad piiMtesaed ti well-regulated d«fitiit« calemlir, 
sutticieDlly certain Bnii predicate to CDHble its beiuy iucor{jonit«d 
in deedft, kBe<:^8, and commercial a^'reemeuto. For centuries tli* 
beginning wf tlie year was fixed by ibo occurrence of the eqaioox, 
and it lA moKt untikelv that Uiey were <tept^iideiit for the 6xiDg 
of this event on the observation of actual New Moon, or on th6 
beliuca] or other fancy rising or setting of a star, when, in tfa« 
passage of the shadow from the Sun over a fixed line on the TompU 
floor 01' conrtyaril, the line midway between the l"Ogest whI 
shortest shadow during tho year, they bad n means of fixing tlis 
date of the eqtiinox to the very day. TheQ, when the equinox fell 
aftor the first half nf the Hxed month, the ytf«r was made full bjr 
the insertion of an intercalary month at th« end of the yuar. Tha 
reckoning of time in this maimer by the dimensiontt nf the shadows 
occurs in the <MrIy bistorj' of all races, and is universal in the Elaat 
even now. The heliaciil rising and netting of starn and the 
nsibility of the new moon would have their ivligious and astro- 
logical KJguification, but so clumsy and indirect a method of fixing 
the equinox v^oul■l not have been used when eo much easier a 
luetliod wiis available. Kccently, every year has bnmglit further 
evidence, in the sliupe of astro no aiical ruicord»i and calculations, tital 
the Assyrians, Ilahylrminnn, and even the early Chaldeans possessed 
a much better knowled<^e of astronomy and mur^h liett(>r means of 
making astronomical oli^ervalious than had been assigned to theu, 
and that they cmild measure epincfas and intervals i>f time with 
some certidnti)', prohnbEy by the eqiiivnlent to a dial on the floor 
of the Temple or its ';ourtyrtrd, as well as by contrivances of the 
nature nf cip|>saniniia or clepsydra. This, however, is beyond the 
present aubje<^t, 

Fuller discussion of the eclipse seen at Babylon '*on the 36tl) 
Sivan " Is useless until the full details uf tbe record are before us, 
■nd it is possible to critically examine tho reasons for aseiKniog it 
to some date in the eleventh century before onr era, for at present 
there exist no data for estimating its value as the record of an 
eclipse at any place or at any epoch. If the record can be 
established a» proving the occurrence of a total eclifise vieible at 
Babylon in the eleventh century before our era, it is nndoubledly 
of thn very hi^'hest importance as fixing both astr4inomical nnd 
chronological elements, but we must have the record with all 
ancillary evidence before its true bearings can be prop«rij 
discussed. 

Mr Coweli points out that the failure of the observations ol 
the Sun during the period 1750-1900 to show any signs of the 
assumed aeculnr acceleration iu its mean longitude may be due to 
the existence of an unknown term of very Inng period. That ia 
indubitable ; and on that basis it must be admitted that theM 




Nov. 1906. MrCcweli, Medieeoal ICcUpses. 



'7 



Lobaervalions of tfan Rati cannot be ftaid to be inroneiat^nt with ihe 
extended liypotbcais. 

The evideoco that has been advanced wrvea to show that the 
facta brought forward by Mr Cowell iti auppnrt of his views can 
be ex]daiiied without hnvinj; rGCDiirffe to a new secular accelftnttion 
in the iul-uii nioUoti of the Earth, ho that the^e facts do nor eultice 
to e^tfibli^h th(> cxiatence of mk^Ii a secular accidie rati on. But if this 
18 all, thyy certainly do not suffice to disprove the existence of such 
a term. If that is to be done, it must be by further direct evidence, 
to which I have no access, though it iiiay exist. During paat 
yean in my researches I have refit^t^dly found evidence nf an 
unoxplaint'd apparent secular acceloration in the motion of the 
Moon's argument of latitude, but I liave doubted it« reality, as no 
explanation nf ii» origin seeniL'd available. The exjiUnatioD 
advanL'ed by Mr Cowell, that it miuht W due tn a secular acoelera- 
tion in thiT inciin motion of the Karth, diil not occur to me, or I 
(thould have tJiketi the necvssury 8tei>3 to obtain the data t-i 
invtf>li(;ati) the matter. Tliis, 1 presume, will be done by Mr 
Cowell. I do not «ee any theoretical RXplanaliori of euch a secular 
acceleration which does not seem to involve threat difKunltiea. Mr 
Cowell'st tentative explanation {Monlklif Noticetf vol. Ixvi. p. 352) 
( think he will find untenable on rt-vicw. 

A'oial Obaenatary : 
1906 August 23. 



The Medusral h>lipse« of Cetoria. Uy V. II. Owell. 

Profeasor Celoria has collected a number of references to the 
total ecUf:wcs of 1239 June 3 and 1241 October 6. He cunsidcnt 
that the former eL-liji.se wa.^ certainly total at Piaccnza and at 
l^iesina, and that th» latter waa total at Stadt and ut KUwani^n. 
He draws ihe limits of tt^tality Bcconlin>; to HansL-n's Tables 
(without Ncwcomb's corri;ctioi3i«), and concludes that theae tables 
ore in serione error at the epoch of the two eclipseit. 

ProfesM»r Celoria'.s dm^rania show tbat the conditions that be 
impoKi are very stringent i>iies. Th<j zone of tfttallty for the 1339 
eelipM is to be difiplacud not les» than enough to secure totality nt 
Piacenza, and not sti much as to de.tiroy totality at Lesina, and 
these liniils are very narrow. They becurae still narrow— '' »• l«e 
remenibered that Hansen's femi-tliameter is conHidur«> 
for i-clipse purp'weK. A uimilar rtnmrk applies to 
1 24 1. Professor Celoria's assumptionH, therefore, 
e<iuat!on8 of condition, onw for each ■ciin-p, in wbici 
uncertaiDty is vury slight. Th^ ■■ ■" of ' 

therefore give an excellent 1* 
required by the mean elon^atioi 

The form of the eqnaiioof 
found. Let k denote, as in 



i8 



Mr Cotoeli, The Mediawd 



LXVIL I, 



ratio of tha Moon*« motion in latitude to the difference of motion 

in lonfjitmie aa seen by the obaervpr, and let SfV - V) and SU be 

the correctione required by thn difference of longitude and by the 
Moon'a latitude. Tliuu the equation of conUiltun must be 

8U-i-5(V-r) = o 

where a is a'const&nt, that depends upon the tables to be corrected. 

That this ia the true eqaation of condition is most easily seen; 
for if SU, 8[V - V) he one sohuion, fiU +kU, S( V - V') + & must be 
augtber solution, corresponding to a Hinall change in the aasumed 
tinifi at which the eclipse occurred. 

Kor any place on the Earth's axi8» including the centre of tiie 
Karih iind the two potea, the [Mirallactic didplacements are con&tanta, 
and ihe value of k will be ±o'io, the upper sign corrcafKinding to 
tlie a»cendiug nude. For inuderuti.' Utitudea k is appcoxuuatflly 

+ o*i4 + o*i4 C08 h 

where h is the sidereal time. — 

Of courAe thiti formula in only a rnuf;h one, but it servex the 
piirpoRe, before undertaking laborituis calculations, of pn^rliclijig 
that the equationii oE cuudition will involve 



Writing 



fiU -0*12 S(V- V) for the 1239 eclipee 
and SU + o"36 5(V- V*) for the 1241 iclipse. 

fiU= ±0-09 8K 
g(V-V')=SD 



the unknown correr^tionH to the argument of latftuda and mwm 
elongation enter in the form 

009 8F-0-I2 SD 
and -0-09 5F-fo-26 SD 

We phal! not therefore Imve any trouble arising from the determi 
nant of the coefHcienta being small. 

Professor Celoria hae obtained the oquatione 

98635 Sr- 5-49U 50- 35''4o 

-5776Z4 ^p- i'4og8 811— -4360 

These equationB cannot be reconciled with the form of mine, which 
haM been justified by finch cLonieiitary reatoning. 

I obtain the following expressions for the difference of apparent 
tatitnd<> At tlie instant of apparent conjunction in longitude, SF, £1) 
being corrections to the values of F, T> that correspond to the 
formulsB in MontUy Noiieet, vol. Ixvj., p. 525. 



1239, for Piacnza 
1239, for Iveaina 

1241, for fitadt 
1241, for Ellwangeu 



0-I3511-009SF+89'' 
o'l iSD-o'09SF-47' 

- 0-25SD + 009SF+ 39' 

- 0-2780 +O-09SF- 57" 



Nov. 1906. 



JHclipses of Cehria. 



19 



Heuce, m order to produce totality at all foar places, we must have 

o'la^D - o'ogSF= -21' 
wid -o-aeSD + oopSF- +14" 

with errors of not more than three or four fieconds on the right- 
hand sides. 

The solution of these eqnnLiona is 80=50', 8F=s +300". 

The v;ilut! of 8l> w a jioiuible one, but tbt* value of fif is utterly 
iuiposaible. It caonot possibly be reconciled with modern obsorva- 
tions. Matters are even worsii if tliu eompirison be made with llm 
present tables. The latter require an even lar^r conection SF. 

I interpret alluisiona to darkneM and tu the appearance of slan 
to mean that the place of ubgnrvatiuu was not necessarily within 
the zone of totality, but wttliin a somewhat wUlor zone, within 
which lint more than abnut turonty seconds of Che Sun's diameter 
vaa visible. 

Now this explanation not ouly iervee to dispoae of an incOD- 
veiiicutly laiHO (Hirrectioii to the forninlee iiuL-d in calculation, but it 
18 absolutely required by the records. For at Alteiizcllo in 1341 
we have the record '^ , . . . eb stellw appitruirunt," and ut Vienna 
we have two n^corda to the siime effect, pjofesAor Celoria cotilineH 
tlie plac>t» to which he aKai^civ black ring's lui hia nmpii to within 
a lone not wider thiin tbu zone of totality. As the distance 
between Kllwan^'cn and Vienna in abnut as great, when projected 
perpendicularly to the ci^iitral Htm, an the greatest width that can 
be a.'fcrilied t(] the zone within which stars appearL'd, the central 
line probably wilj< about ci|uidt8ta]it from the two plucci. This tita 
my formulae welt, but 1 cannot u^o the principle to discriminate 
between my forrautjB and the prejteut tahlns. 

In 1239 the record at Milan baa to be rejected, as Professor 
Celoria snggests, on the yround that the writer lived 160 yearn 
later. We are then left with the records that stars were seen at 
Piacenza, and thiit tin! eclipse wna certalidy total at Lesina. 

To gnui up, ihon-forc, my fonuulii cannot be accepted unle&a 
it he admitted that at I'iacenTa in 1239 atam might have Iteen seen 
with about 20' of the Sun's diametiT visible ; on the other hand, 
if the theoretical eecular accelenition be altributvd to the argument 
of latitnde, 30' of the Sun's diameter would Imve been risible. I 
am not prepared to Hay that 30' is poMibleand 30" impoesible, and 
thert'fore no prouf can be bused upon these tcUpaes. 1 feel bound, 
however, Vj vxaiuine alt evidt^nce that 1 come across, and 1 can 
only say that I am perfectly satUKcd with ihe «ra ray 

formulae stand thi; teat in the present infitaucon. 

The outline of the calculations is as fuUnwa:- 



Chaiiges in a Julian c-r']— 



True Longitude of Moi 
„ Sai 
True Etuugation . 



■. " ro' 



I3;0 



H 20 Mr t'omll^ Tht Mediccval 




LXTIL nfl 


^^H. 1339 


1 


341 m 


^^^^^H Plaoetm. I^alnit. 


StMlL 


BllirmngM.^1 


^^^^^^^ Parallax in Longitude . 55'j 55V 


45"'> 


49 J H 


^^^^^^B Appureiit ElouK^tiou 130*8 130*9 


i4i"6 


'37'' ■ 


^^^^^^^B Geocontrtc Latitude of Moun -h i8~42 


— 


18-24 1 


^^^^^^^H Paralliix in I^atitudB ^ j'2 " i'3 


-177 


~ 19'^ H 


^^^^^^^1 Apparent Latitude 




fl 


^^^^^^1 


-359 


— 37'8 ■ 


^^^^^^H Hence A' .4- 0*13 + 


- 0'2 


5 - o»7 


^^^^V 1239 




1241 


^^^V T in uerituriea from iSoo Jau. 






^^^H 0-06 MT .... -5*6054754 


55820399 


^^^^H Cr.M.T. in degrees . +3**9654 


— 


2'-645i 


^^H. V • 


169 


28 27-5 


^^^^H 


357 


3 269 


^^^^H ■ 344 36 


7 


50 14*0 


^^^^^H 39 


292 


»8 35*7 


^^^^H 2^4 51 


33<* 


1 1 20'6 


^ Inequalities of Moon's Longitude :^ 







^^^^^^^ a. 21 largest terms, coetticioiita over 20' - 5096*2 


+ 3299"* 


^^^^^^H ^. 30 next largest aolar terms, co- 






^^^^^^B 


5-9 


+ 535 


^^^^^^f y. 58 next largest soltir terms, co- 






^ etKcients over o"*i5 ■ ■ + 


4-0 


0*4 


^^^^1 8. Figure of Earth terms . + 


7'J 


+ 3» 


^^^^1 loequalitieii of Moim's Latitude : — 






^^^^L a. I4lur^est terms.cucEHcientsoverio'' +1271*3 


+ 3 1 1 80 


^^^^^^^ p. 42 next [urgBKt solar ternifi, co- 






^^^^^^1 ellicionts over o''55 . 


2ft 


- 63-7 


^ y. 62 next Inrgest ftolar termii, 00- 






^^^^1 etficienti* over d''o6 . 


0*4 


- 3"9 


^^^^H S. Figure ul' Enrtb terms . . — 


7*5 


+ i*a 


^^^H Moun'sRJnt ^anilia.\. Constant, 342f''*7 : — 






^^^H a. 5 largest termit, coefficients over 10' +3671*5 


+ 3678*7 


^^^^1 y?. 9 next largest solar terms, 00- 






^^^^1 elGcients over o'*55 . 


09 


+ 4*2 


^^^H y. 1 7 next largest wlar tuniis, co- 






^^^H efficients over o'''o6 . . + 


i"o 


— 0'2 


^^^^ Inequalities iif iSiin*« Lnngitude: — 






H Thrcetcrmsofequatiou of centre + 33' 3;; 


'1 - 


'■ 49' 7'-7 


^H PliuTiiza. L«B!Tia. 


auuit- 


KlIwanKcn. 


^M Geocentric latitude 44''5i''o ^2''^S''6 


53 'H '6 


4S°4S'-6 


^M Radius Vector /> *99830 '99841 


'99779 


•99807 


^m Longitude, East of 






^B Greenwich . . 9*4i'*S5 i6*28''23 


9'28*-43 10V9* 1 


^m Parallax in I^>ngitudc : — ^ 




4 


^H a. Terms of first order- 740*3 -1055*0 + 


8501 


+ 736-7 


^M ^. „ second,, - 11*9 - i6'8 + 


7» 


+ 69 


^M y. third o'2 - o"2 + 


o*a 


+ Q-* 



Nov. 1906. 



Eclipses of Ceioria. 



21 



, VamlliiX in Latitude ; — 

'I a. Termaof first unler- I339'8 - lajo'i - 3i22"2 - 30067 

fi. Smaller terms - i'4 + 0*2 - o'j + 0*3 

The formiiliB used fur the arjjumeiit« are those given in 
Jf. N., Ixvi. p. 525. 

Tho iuoquuUiiea of the Moon's longitude. Latitude, and 
Paraltitx are taken from Brow», J/. .V., Ixv. p. 276. 

The ine(]ualiLics of the Sun's Longitude amt the obHqutty of 
the ociiptic are taken from Nowconib, Tables of the Sun. 
The tigttre of Earthen terms ui*ed are -. — 

r Moon's Loiigttude+6'*6iiin n - o"'? &»n+ I'-osinncoB 

r Moriti'ft Latitude — 8'"i siu L+ i''5 cos L- I'-osin t?co8L-o'*3 8iD (F- fl) 

Nutation is not applied, since it h the siinie for both Sun and 
Moon, and not sufru-iu'iitly important iu its clk-ct on iho [laralUx. 

The planetary inequalities have not been calculated for either 
Sun or Moun. 

Tbe formula used for parallax are 

q = p (sin p-p) 
I Parallax in longitude ~bq - ahq^ + (Ji* - a^b)q^ - \bq\3^ 

„ latitude - ft/ + (i//(U - oj) ~\yj^ 

where a = cos A cos A cos V +coHA6inAco8e8in V + sin X sin «8inV 
6 = - CDS \ COB h Hin V + cos k sin h coa c cos V + sin A ein < cosV 
I c= - cos \ sin /[ sin c + siu Acosc 

Leiw cXttcl 'tailciiliitions would have been suflieieut if 1 could 
have foreseen that llie only result is that my fortimlie expose less 
of the Sun's disc at the places named as places where stars appeared 
than the theoretical forumla:. 

The present paper is most easily read in connection with 
Profo»8(.ir Celoria's diograma Tliese, however, can be sulGcic-ntly 
rp-prottuced from the following extravts from Frufcssor Celoria's 
papern, The latitudes are geogrupbicat. 



1239 June 3 

North 

43' 6'-84 N o' 2g'-79 E 
44 18-97 8 33-34 

44 43 So 17 I -14 



1341 October 6. 
North 



46 

and 



58* 35'-96 N 
5« 57 '27 
37 08 



6" 42'oi E 
12 48*14 
17 24 99 



Limits of Totolitj. 

South 

' 49''S3 N i" la -58 E 
41 58 -58 8 33-51 

I 42 24 -64 16 34 '23 

Limits of Totality. 

South 

• 56'-48 N 4" 59-05 E 
4 1 '56 JO 49 '69 

34 64 15 • 



Ptaco. 
Milan 

Attenzelle 
Vienna 




lAtltud«. 

45' 27" 59" 

SI 3''SS 
48 12 55 



22 Prof. Lamwr and Major Bills, Tlic Irregular Lxm. I, 

The positions of the other places mentioned in this paper an 
^'ivoH abovL', 

Professor Celoria's extmcts from mediieval records represent ■ 
voBt amount of Tatnabln kbiMir. It i<i advinable, however, to warn 
readers that hi'* figures for the 1239 eclipse must not be ttiken from 
bb origioal pii|>ur, but from hin ovru revloed figures in hia aecood 
paper. 



2V*< Irregftiav Movinnent »/ tfie Earth's Axu of Rotation: a Om- 
tribiUian fowardt the AnaJi/^'" of its Ottusng. Ily Profeaaor 
J. Larmor, F.R.S., and M^'or E.' H. Hdk, C.M.a.* 

Mneh material, defining with increasing aocnracy tlie irregulnr 
wanderings of the Karth'ii axis ol rotation, haa no»' )>eeR iiccnmuUt- 
iug for a long series of years. Tlie attempt to deoompose the 
moveuiLMit into regular hartnonio ci)m[)orLui)l.s excited interest some 
six or eight years a^o. Siuce that time the more sy^tL-matic data 
obtained and analyned hy tho International Organisation have Kiren 
greater precision to the phth of the Pole ; and, while a definite 
astronomiciit ilincuasiou inuab rest with the fxpertH, ctirin.tity ax to 
the (^uueml phyctical causes of the pheuoiuenon in Itrgitiuiate. It 
h&a lou^ been recognisfd that di-placcrneat of material uti the 
Earth's enrfrtca due to meteorological changOH (nielting of polar ice, 
llong-period barometri'.- fluctuations, etc.) must be a prominent 
agent, and may itiileed be taken to Ik the umin one; while New- 
comb haa pointed out that the free Eulerian oscillufcorv period 
rau8t bi" very ditTereut, for a niMirly spheriiailly balance<l Earth, if it 
is ela^tically d<.-f(jnnablo under the centrifugal force, from what it 
would be if it wore rigid^ thus accounting for the unexpected value 
of the Chandler peri ml. 

It is shown btlow that, without making any hypothesis except 
the nntur'il ont^-, that this free precesKioual period h fixed in 
duration and determines the average ilnration of the revolutions of 
the Pule of rotation, it is easy by a graphical process to deduce 
from the path of the pole a map of the varying torque which mm 
be acting in t'rder to pniduco tbut path, and tlieoce tu infer aa 
llie cimracler of the displacements of terrestrial material that im 
be taking place in order to originate that torque on the Eailh as 
whole. It has seemed worth winle to carry this out iti a p: 
liminary way. It has also beiin thuu;,'ht worth while to nut do\ 
various dynamical coiiaiderations wliich may prove useful in 
systematic analysis nf the ohKervationa] rt^nlts. 

Let (Up tti^, (i be the component angular velocities of the lijirth 
referred t<> axes moving with itself, the latter lieing around th< 
axis of figure. Thus taJQ^w^lQ are the angular co-ordinates 
the pole of rotation raea.4ured on the Etrth^s surface, and repreac 

* Read iD psrt at tha BritUh Auociation, August 11>(K. 



Nov. 1906. Movement of the Earth's Axis of Rotation-. 23 



diroctl^ the cliBiiga of latitude ; tliey are dtlfcrent from tho abaulut« 
co-ordiuatcs of the pole on tbe coleatial apliere, in the urdur of the 
ratio 0/(C - A), iw appears from the I'oiiisot geometrioal reprosenta- 
tioD of the fre« precB&aional motion, C and A being the effective 
polar and equatorial niumuuts of inertia.* Tim dynamical equatioiui 
of tlic Earth's free pnscessioii are, witli auflicieut accuracy, in terms 
of the angular moDientum (A,, /u, U), 



dt " 
dt " 






where, D, E, K being prudncts of inertia, 

Ai = A«, -F«i,-RQ, A, = B<.»3-Dn-F.,i^, H = Cn-D«j-Ewi 

Thus A<b,-(C-A)U«>j= -L' 

A6,+ (C-A)n«,= -SI', 

where n may be taken constant, becansa its variation would 
miiltiply in Iheae equations two factors, aaoh Rmatl of tho Ant 
order ; and whert; L', M' include, in addition to the kin<itic furcivca 
doe to tho locution of mobile muk-rial attached to tlie earth, the 
terms 

A«i - tu.j -tu, lj(«j - t>u - t«i 

Here tho termd on the left woiiM bu nitv^i of change of angular 
mtimontuni if the coiifij:unition remained wnsiant. Tbe terms on 
tbe right include the revurxi-il rate-^ of change of tbe name, taking 
the angular velocity ounatant but tlie conBgnration altering. To 
determine these latt«r Urm^, rh ari»in;{ from the reaction of 
mobile terrestrial maU'rial, we am conttider them directly as repre* 
scnting the centrifugal forces of this loose material, tcigetlier with 
the reversed gradient nf the an^ulap nionicnlum, due to tlie Karih's 
rotation, of new ne;^ative material in the original position and 
of new positive mat^^rial in tlie altered po:«ition. 

Tho difTerenue bQtweea this procedure and the asual one 
adopted by previoua writers t is that tho investigation of tlie slight 



" (y. KoBth, Dunamiai, ii. §5 i&o-a, $^3, 
of this fMCtiir C/(C-A] thn uia uf roUtion 
except in so far u the cxtTAneouft Attr:x<rloni *>' 

CKUKini^ rorccal lirw^vwi'iit. m tlinl tli« Bffl'Ot 

of iatiiudu. Cf. Haxwrll [" On 11 Itj-natr 
tioim 09 to the Bartli'* M<ition," Tnnu, 
i. (pp. 159-^61)], who appear* to h^vn ' 
tliAory pncuely m tlie Rnrth, aiid to ei 
•Mroh of « 3a6.dNy poriod in latitml 
Monthly Notuta, Hi., 1893. pp. 3^6-41 
thia periocl, itiHihilrd nt Pulk<iwa tiy f 
had alresily }-i«1H-' I i--'-'- r...,,if. 
niit ai)d estitiiLi 
yielOinfr, the ]i<: 
considered. 

t For an ucDUt) 



On accotint of the tarfCflTiess 

IS [inii'ticiiliy fizi'^t in spo^, 

tha Sou and Moon opsmte in 

ilioii in xiniply & oharijjv 

. with Home BngzM' 

^P ScienlijU Papers 

l^ply the Entcriat 

Irh obsirrvittionB id 

'rof<«»or Newoomb, 

" th« Utit\Me, of 

Tt«ii, ill 1S62-7, 

vrliii:h pni[it«d 

U"-**! Ijy elastic 

DienU wiu aim 

^ ^^ SVrV 



24 Prof. Lajrmor and Major ffUU, The Irregular LXVn. 

chan^fea of posilaon of the Rarth'H [u-innipal axes of inertia ariaii 
from displacement of material ifl evaded, by conaidenng an un- 
chaiii^ia^f Earth, witli effective ti)omi.'nt!i of inertia (A, A, C), which 
id subject to force arisiug from the kinetic reaction exerted on it 
by thift additional and iDdepeiident niat^ritil, ituiving over it and at 
the same time maintained by it in diurnal r<iUlion. 

The L'ffetrt uf cenlrifiiyal forcu, in flatUiuiag clastically tht 
terrestrial Kplicroid, jiiinply modilics ita (effective or dynamical 
momentti uf itiurtia according to the (iriiiclplu arrived al in a previotu 
discussion,* viz. tbnt the niomt-'iits of inertia which would exitC 
in the alisetico of tliurnal rotation, but on the assumption that the 
E;irth'8 form wheu centrifuniJ force ij* thus removed ia determined 
by a linear law of ehisticity, are to be employed in dynamical 
investigations which taki^ account of the clastic yieldiuf; of the 
Earth. Tnere wmihl be cnnseqiieiitly an increase in the frtMj pre- 
ceasional period (tictually as obiiervoii it ia from 506 to about 438 
days) in th« tnntvner lirat pointed out l>y Newcomb. 

Kefer now tho problum thus foniiiiiated to axw of w, and tn. 
rf>tating with angular vs-locity n(C - A)/A, that of the UDdiulurbed 

• "Oq tin- Kirtli** Pre© EuleriiiD ProcossioB," Pror, Camb. Phit. Sbc, 
Hay 35, 1S96, p. 186. 

The srKiiin«nt there eniptoyetl, brieifly stated in more analytic form, ia a« 
follnwii. Let A', B', C be tlie }>rini!ipa) inonistits oT in{.-rtift of tite KaJtb 
whi^ii iiu^traiiiail liy oL-ntriliijlfal force ; uid Itrt I lie thtt chaogt? of moment of 
inertia rouud its awn axiii, duv ti> tliu equatorial pretulicrauL'« rtuwd by ihit 
foTott. This miA ia ia th« direotiun of the rr-nuUftiic &ii^u1«r vt^Iocilir 
Co»i , wj, Bj); uti'i It is ii[iplii:i] tlinl it i» vary near tn tlic principal axis of 
greatcKi mamitnt C, ^o that n/ = n) in yiracticAlly i-ouiitadt And f^r'-at eom- 
fwred villi «, mm) «>,. It. is mvuK'til aUo in lliit rttttrirliiiTi that [ u a 
oftostant up to the first p'lwer or »,,'fl or ajti. Hcferred 10 the principal 
azM, tbs bitiil Qouipotieiit uiif^iilar tnomeuts are 

Tho (Hjoationa ot motioa reforro<i to the rotating az«H ara of the ««U-knowa 
*Mtor tyiw 

Whan A and B ara Aqual, th* third of tham ia 

where C in tho elfectiv* moment of inartia C + 1 : when N i» iinll m, ia th| 
ooflstant, ftay C, up to the first ordor. The other two oq^iiatJoiitt are 



^.(A'+IV,+(C 



ll')n.»=L, 



A 



.(B'+I)«,-CO'-A'}n», = M, 



which in the cam of approximate Rymmetry invitlvu a fri>e p^rit/ 
Jv(A'+ I)/(C' - A')a, &n<l HttnUitrly in the general caae, tbtu depcDiling on] 
on A', B', C wh«n I ih small. 

The piwcnt pnu-eilura ahitorlut Lhi* tfTwl uf ihin rcjjular changi; of for 
due to strain irto moiHGed mamenU of inertia, while it MCa ont the enbct 1 
erratic (iiBplncemoiit of [additianal] tiiaterial on the rotating Earlh as 
hinettc roroiva. 



Nov. 1906. MooemtfU of the Saiih's AjPis of Bolation. 35 

fr«e Eulffrian precesciiun, viz., about 438 days. The equations of 
movcmeat ussume the fortn 

A«j = — L', A<i>n « - M , 
llie name as If the axes were iixed aiiJ there wer^ no diurunl 
roLHtion ; that is, the (lokr axis moves in the oartb, relative to 
thi'se rotating ax&s of o-vnnlinatefi, aloiiy the direclioii of the 
revfraod ri-sultanl of the ton|UC3 L' auJ M'. 

It RPems useful, therefore, to ])lot the course of the I'ole relative 
to c<M>rHiiLate axes rotatin^^ with the mean Chandler |iQr>oil, 
tiiarkiu>{, at intervals ulou^ the curve, both the time, and the 
loiiyitudc of one of the ruyolvirig axc« of co^rJiuutes at that time; 
for the velocity along the curve itt any instiiut will then give the 
direction and magnitude of that part of the rate of change of 
(L', M'), the transverse coaiponeot of the centrifugal torque of the 
lotise material and tht! tiuiegradient of the angular momentum 
arising from transport of this material, when the velocity of rotation 
i^ imagined unaltered. Huch change can tliereforu he partially 
hicated, as infra ; if it is mainly due to displacements of surfoce- 
matertal, uf thermal or muteoroluglcal tvpe, it iihould whow tmaaonal 
recurrences, and may prove to be in part due to .''light change in 
ocoanie or barometric levels. 

^SgreK&te rouKh eittiiuateii of mere onler of mu^nitude are 
easieab made dia"ctly, without use of these rotating axes. Thus u 
BUrfac« depression of i foot over a aquare mile, extending down 
in gradually diminishing amount to 30 mileft, would involve an 
effective displacemeiit <>f a layer i foot thick through 15 milea 
downward. In latitude 45', where the effect in Uuh respoct 
M'oiild he greatest, this c1is[>lacemeDt would change the resultant 
trantjverse compoueiit of angular momentum of the earth by 

4000 O ^ — a co«- 45*, the whole ani^ular momeutum of the earth 
5380 

bein^ in the same units 12. 3^. j^n-(4ooo)". 4(4000)'; this takes the 

deaaity of surface material to be 2'^ and thai of the whole Earth 

5^. Xlio polar axis would thereby he displaced through an angle 

equal iti absolute meaAure to the r^tio of these ritiantitieK-, in 

seconds of arc it would be about 3.10"'^. Thus local displace- 

mcDts by earthquakes can liave no st^n^iible ilirect effect on motion 

of the Pole. But more important is the centrifugal cflTect rep' 

seiitable liy diftplacement of the axis of inertia of the El* 

round which the free precession of the polar axis is taking < 

This angular displacement is A/{C— A), when h is ihe prod 

inertia thus introduced : this is of C/(C ~ A) times (ahou 

timefl) the order of the direct effect on the I'ole of robttiim, i 

in the present way of viewing the mat* m or 

precession is praclically everything.* h" 

by Milue (Bakerian Lecture, Rotj. Soc. 

* 8tr G, IT. Dunrin hii^ r«crtitlv rxpreuM 
t>i« et)eot of e«rth(jii«kra may bn to bring th 
axis of tigaro, and chu« damp the iwJar roovt 



26 Prof. LarmoT and Major HUh, The Irretpdar ixvu. 



•mall range of time (two ^trars) tlien iiive8tigat«d by him, sbarfl 
curvatures in tlie polur uiuvtiuetit apptwrud to be oti llie wlioM 
concoiiutanC wilU earibqunkes ; the latter may be protnoled perhii|«.j 
bjr tlie otianf;e!i of sujmrlicial or intvrnal Inadiiij; along meridiaiu^l 
bbat arn tito iHAin cause of tlie irre^'olar motion of the Pole 
are greatesL wben the curviiUire of iUi path is sh&rfiest. 
procedure indicated in tins note would Incntt- to some extent thi 
displsceaient or chaij;;e of loadiufti itod thus tu»t tlial theory.* 

The ciVoct of traiisfor of water fiom the Poles towards mi 
latiturli's, uri»iiig from melting of Arctic ice, may b« efttimat 
Bitber by cotittideriiig art added layttr, of tbicku&u positive 
negative according to the locality, und of null u^'^re^ate amount 
spread ovt;r the whi>Io ocran, or by estintaCiiiK directly oh obuvi 
the cbanga of angular momentnm invulveil in the diitpUcement 
each portiou of tbo material. A difplacement of the Pole 
rotation in the Karth in a given direction, whvn referi'ed to tli 
rQtaliti>: axes as abuvo, would imply idtorati'm of intrinsic angul 
momentum of eiirfnce Irwd in the noighbourhood of the meridii 
circle containing that direction, wlii«h would ba a defect in tl 
northern qiiadmnt in fn-nt of Chat direction or an increase in thi' 
norlbeni <[umiraiit behind it, anil vice tvraa for the uouthem 
qnadrants. . Thnx wat+;r rapidly moved from the Poles, where 
has little angular mcimentiini, so as to covor to a depth of i fc 
a region 4000 nii]>es square, in middle latitudes, would diaplaoe 
the Pole of rotation in the Earth by something of i\w order of 2 
Mjcoiida of Hrc; for it would involve a new transverse angular 
momentum Ji cos-45'' 4oooVsa8o in the same units as aburei 
It is reedily seen that the principal axiii of im-rtia, about whtch 
tlia free precession miuld continue, vuuld he displaced in the 
opposite dii-ecliun tlirutigh an angle of the aiune order. 

In reducing the International Observutiontt of cbanj^e of 
latitude at the (^elected observatories extending round tho Karlh, it 
has been found necessary to imilndo a chnuge common to all 
Inngjtudfs, which at first sight could only arise from change 
of form of the apheruid which represents the terrestrial sea-IeveL 
This miglil ha in part due t(.i gravitatiaiiu! iutltionce of the displaced 
material ; yet the removal by molting of 10 feet of ice over a polar 
are.i 500 mites in diunieter would produce a chun^e of attracUou 
wliich could not, in middle latitudes, raitie the Pole by more than 

■ Tlir pjwc \<pTv consiflrrod is 15 euliie milcB of matorial ilit-pUopiJ vertioally 
I foot. I'rotcsaor Milne iuforms ua that tho rcauU of tm Actual aiirthqnaka 
midic b« ro.ooo.ooo cubic miles tHspluceil rortiwllj or lioiijantally tbrottKli 
10 tMt. This would multiply iho nifure tti the t«xt by 7.10^, thus i^iving 
2.10-' si^oTKJR of »rc Aftrr cbia (imlii.n nliift of thu axi-i of n>tati>>Ti in tti« 
Kiirtli, tlie fre« [ireceMiDnwould ooiitiiino, but it would be arvnnd a turn 
|irini-i|iul axis q( iin-rtla dUpIacTrd from tha orE^iiinnl nno l>y a qttatititjr 
tbfl Mine aoiall nrder of magnitude ranlttpli^i by C/(C -A), that ia by 
giving a result ol the ordar 10'" beoonds. 

Sir G. H. Diirwin has Mtimated (WiV. Trans., 1876) timt , |t, of 
ATM of Afrioa riiiiaj; or falling i'h $iiH througb 10 feet woaM i>T4duoi) 
Eoooiids of chuntfe, the rising or »inkin); hfitig [in-auniably talceii as 
lui-rely luperGciii]. 




Nov. 1906. Movemcni of the £arth'» Axis 0/ Botation. 27 

l/iooo of the order of luaRnilade requiretl. As thL- ufft-el seuins to 
be re»l, some iiidtrcct, p«rha[>» aeus'iuol in^tnimental, cmifte nillfit 
appan^ntly be flight for. 

Ill trying, as here, to separata out the roeteoraIagi<A] displace- 
niemtii ot ttic Pule from tbe triiu free [>rece«>aioii wbicli tvuuld in 
thi'ir absence be a i-c-gular circular niuiioii, by referring the whole 
to rotating axes, the L'^ential point in to assi^^n as correctly as 
possible lift jwricid of this iirvcussioit, for thut dctftrmiuea the 
velocity of rot-ilion to he given tn the axea of ro-ordiiiftt.!(i. Klastic 
yieldiug of tha Eurth will proUnij;; the period beyond the 306 dsya 
thai would beloug to n ri^id solid. Hougli hiis shown * Uitit an 
Rseragc modulua of rigidity of a solid Eartli even so ^reat as that 
of ftteel would involve the prnlongation of the period to the above 
value, 42S dayd, which reprpsentj* the p»-riodicity of the observed 
putli i»f the Pole. Now whatever be the caune, fiastic or fluid 
displncement, or both, that thus alters the flVective dyiiuniical 
momentB of inertia of the Earthy it nmy be {in^nimieil that it altera 
them to a constant exUint i>ver a fairly loujj peri<»d nf tiiiie Tbua 
the true free, or Kiilerian, precession would niaintaai a rotation of 
the Pule fairly coiiittant, while the nieteoTohi^ical dinttirbance 
atipftrpfjsed on it would in the lung-run have no rotational qtiality 
ona way round or the other. In applying the ntethod of snalytis 
of the complex motion that is here proposed, the angular velocity 
of true preceasiun may therefore he obtained by taking the mean of 
the observed tiiuesi of revolution of the Pole, as Chandler originally 
pointed out. 

The Eulerian principal axeit tixed in the Earth, or still better the 
axes rotating ax Hpecihed ubovL% arc aiiprupriatc^ to Lht; analysis of 
the effects of nioraenia or Uirque-s which arii»e from change of load- 
ing and are therefore thtniselves revolving uu the whole wilh the 
Knrth. Oil the other hand, torqiios which only slowly change in 
direction in npare, anch an thosH aiising from the attraction of the 
8mi and Xfoon on the protuberant pnrta of the oblate terrestrial 
tipheroid, are most amenable In dynamical analysis when referrod 
to fixed axes. Tli^y jiroduce inaioly the Dulinnry fori-ed astnmo- 
uiiod prwiesaiona and nutations, on which the varying elastic 
yielding of the Earth hati no gen^ible kinetic intluencu ; while the 
intensity of the ti^irque of attrai;tion depends on the inKtantaneoua 
l.'eoni(itrii!al value of C - A, us dctermint^d Vjy distribnlion ninne. 
The diAtrihntion of maas thus governs the Hilar nnd lunar pre- 
ceasianB.t These forced preoeMions depend on internal fluiflity, 

* PM!. TVan*., 1895. It ia (aa above) the near ikppmu'h Ln8|iheri' ' 

m&kes sa kliftht n yitrldiog to the changes of centrirugsl imd o* 
«ff«otive in this manner 

t Tliora U UT1V raxH, howevrr, iD wlikh, as the equsttoQ" of 
above bIiow. a BriiAil extraneoatt foroivn would tAU)w> a wnnderin 
in theEartlt itw-If, iiiu<;h gn-aU-rtlian ilii (])»«£•■ iir-lnection in % 
th« aBtrooomioil prec«>iion thereby oaUMd. triat. uamoly. of a f 
■ period in loRgitiide reUtivt* to tlw- tJirtli'i* rtxntioii, of tha 
frae perioil of 426 days. Such a t«nii iu the roroivv vuxiVd > 



38 iV^. Larmvr and Mv^or IIUU, The Irregular LiTtl. 




etc, only m so far as it modifies tbe tfluillve itionia-mumeDt C 
or A ; while, oo the other hui-). tbo frpc iirccifHuioii d^iieiula on the 
elfeotivs or kirK^ic valua of thn sinaU diflVrenoe (G - A);C. 

Tbo tides would be itUiiul the same at u)ti|icM]al poiotA U oon* 
(oun of the land wen vymmclricol, and the two opiKwite tidal 
protuheraooee would be iid'hliTC in their effect vii the free pre- 
oewiooal momeDt. At flr«t sight, it might appear that the catiniAti' 
given abovft Tor a local oTerflow of a fimt of watfi I'roni ilin Vo\ar 
reffious wuuM involve thut, even ajiart from tbc irregularity of foroi 
of ibf <H.enii», the features of tho vnnous tiilnl u-oiniKHicnti travel- 
ling rnuitd dm Kurtli niUAl he n-priMlticrid to some vxtfiit in an 
t-xtLcX diiigmtn of the ttirqnr, ovrinK to thu tidal flow demanding 
nltomtion of tho nuKulAr momontum of tbo water rebaive to the 
Cnrtb'4 rotatiun, nii<l to it«i centri futjal furc". Hut in m* fur an it is the 
Earth that turmi round undvr th« nearly atatioDary tide, the dirtet 
dynamii::al uHvcIb tif tlie tidal rooremeDta are very alight and belong 
to thi9 iMlrunouii*:al clau, aud are in {act merged in the lunar and 
volar nutationH. Itut if Ihu Karth'ii Hiirfact' wcru dividt-d by meri- 
dional bitrricrs, au tlml lbr> tulal Ibiw would Iw in llie muiii north 
and south iimitfO)! <if around the Kartb, «<• mincht i-xpe*-'! a tidal 
aberration iu tb*> latitiido of amount not entirely inaeniihh*. 

The mnx'riilude of tliii tid»l torciue would then rt>Di|)ar« otmi 
with that of the preceHntuaitl couple of the* Muou'h attraction on 
tho prol-uWanl portM of the terrc«Lriat spheroiil. The latter ia 
\ Mr-'(C-A)«n 2S,N>that iUamplitttdiMHabout^(o'*i9/(]) io-*C 
while the earth's angular momentum if* (.V If this torT)ae were 
to rotatfl with the Karth for eiz hourH it would pro<luce ati angular 
displacemoul of the Pole of amount o"'ooi y.bhiiMi, where i^jg^ 
g^, that ift, uf amount o"'ooi x 289.^7 or o"'5 ; in contrast with 
the aotnal lunar fortniglitly nutation of amplitude one or two 
aeooodiL It bax just bein mmw that a partial tidal overllow from 
the ikiIm cuvL-ring (4000)* iqaan mileii to tli« depth of a foot, and 
earned on with tb« ICarth'H rotation, could in an extreme cau 
account for a iliftplaci'ment of the Pole as miit:h a« 2" : and the 
antipodftl high wutrm rviuforre each other. It is inn? that if the 
tlarth W)'rt9 covered «ymmetriealty with water, the Sun anJ Moon 
tntvelling in the equator would proiluce no oflecL Bat the 
oblii|Qity of Ibfir |>«Uia and the irn^guliir distribution of th^ oceans 
must load indirectly to mttations of the ^ kiIo of the short periods 
of the variouii tidal coniftonents, which are not insenMhte in the 
present <u>unectioii. Thus, for example, a fon^ed nutation of this 
kind might iutivduct) discre{iani:ies into ubicrvations around a 
parallel of Utitude. of charaoler in part sj^steuiatic owing to the 
progrcsaive «->nit-ditin)nl chnn^'e of phase, wbirb would beeliminatcd 
in muoihiug out tha obM^rvations for cmch observing station of the 
IntornatioDBJ chain of loDgttude. 

PtMMibnitim in tbia direction are perhape worth Iwaring in mind. 

(■dlUllun it* Utitads of its omt jmrioA. whieb maid ba MiprruMcd on ths frse 
oMfllatloD ef a usarly «qoal period, thtu prodooiag an altfrastloo ia tU 



I 







*^-^i 



LmcO* 
1. AURECHT. 1900-190$ 



lacr 



9orw 




eorc 



2. Albnkch-i. l8S0-t641 . 



MOhTMLT NOTIOES OF R.A.S. 



Vol LXVII Pl*tb 2. 



IflO' 



9orw 




3. Chanoler,. I895-1S99. 



9a*E 



160" 



&0V 





% 




v^ 


^ 


/y% 




"^^ 


A 



UmGT 

4. CHANOkEfi, taao-n 



9<rE 




ov. 1906. Movement of thu Earth's A:cis of RottUion. 29 



example, in addition to the diflferenoe of pboRe at differeitt 
itioiis mentioned aliovi^, if tlie samo 8lai'» were observed at all 

fttations^ a Bular tidiil nutatiun mi^'iit partially simuliite » change 
of latitude witli a yearly pt:rioU, L-otniiiou to uU thu statiuiu, such 
as appeam in tlio reduced observiitione. The deviiitlmi of tlie 
vertical hy the attraction of thti ttdal wat(>r \» in all cuhoh very 
smaH compared with this deviation of tlie Pole {cf, Thomson and 
Tait's Nittural Philosophyy ed. '-*), and i« in fact here negligiMe. 

The indnence of a nutational tor>{Ue of fairly short period could 
be laid ofT by aid of tbe dia;;raui referred to rotatiQ}{ axes; but 
even in tbis case it can be effuctL-d rather mote easily ia tlio neuul 
aatronomical manner, on account of tlie relatively nluir change of 
itn direction in sjiace. 

But whether these tidal influences are sensible or not, assuming 
428 days to lit) thu pi-riod of free precession, we can transform tbe 
cnrve of wandering of th" 1'oIh :is shove to axes of co-tinJinntes 
rotiitiag will) thiK perio^l : and the hodograph of thitt new finrve, 
when referred hack again to axes connectt-d with the Karth, will 
rt^gtrciient the dimribtitiun in direction and time of thu torque 
arising from displacement of terrestrial nmteriiil, which is con- 
tinually modifying the nmtion of iho Pole. Fr»iin the puirit of 
view of genphj'sics, lliis cnrve would appear to lie worth setting 
out, and might bo expected to show scusoaid rceurrt-nws. 

The annext-d diagram (1) gives, from the path of the Pole since 
1900, aft ofticifilly pubhfihed by ProCciiflor Albrecht in the Ati. 
Nachr.t* the tori^tiB which must have been in ai^tion to caiiAe that 
motion. It will be obbi-rvud that the expected annual periodicity does 
not appear, but thut the diructiun ot tbe mxia of the torquu puiut» 
preponderantly towariis the side of the Pmific f )ei!rtri, an F-xtraneoua 
feature which wo tthull show how to eliminate later (p. 31). 

Then follow, bnt liawd on more imperfect ilata, the torque- 
diagram (2) derived from the Albrecht diagram of I'olar wander- 
ing ft>r the period 1S90— 97. The other two are derived 
frora the Chandler diugmuis for the period^ [895-99 and 
1890-97. it will bti noticed that for the first one and u half 
yean of the overlapping [>eriod 1895—97 the torque-diagram h 
much the same in both, but not for the Uter part The appearance 
of all these di^oams is vi-ry different from that of the kni, e.g. 
the one-sided biait in the torque does not appear. 

The unit (o'l) uiarketl on the axes of the diagrams represents the 
torque that would shift the Pfjlc at the mte of o'o5 in one-ten**' "' » 
year ; tbe dat^is are niiirked along the curves in decimals of 

The analysis of Chandler made the motion of the i'ule 
his cin^ular precuriaion of 428 days period, with anaddjtioti 

* The most t-onverripnt vaj %a una thew disjpi^DS n to pla* 

tfrreBtrUI j{l»*'«", ""ith lh< origin at th« ' 'ihrech' 

l>Ath-dia<;r'iiite from whioli thmt roTce-iiu 
fcHinil Ml Btrirht Sber lUn Hiand . . . t 
vol. xiz., rM|>«cdvely. 



30 Pi-of. Lariiu/r and Major Hills, The IrreyuUtr LXTIl 



motion about tba centre, and of yearly period, aaperpoaed on 

Tbe compontrnt tortjuuii that would uri^jiiiiate 8ticb an addillun loj 
fruB ))r(.'C4><»Biuii vl 428 Uay», beJug proportioDoi U> ^i^^ — nuu 
u).,+ »W|, vvuulil biive an aniiiiftl elliptic jieriodicity, in nitigh 
mt>nt witb thin diagram. For, refetring to tbe axis of the Alt 
tbu theoretical motion would be 

w, = A CI* (nt + a) + a co-i pt 
«,, = A sin (nt + a) + bsinj>t, 

«o that d»j - fiw, <= - (aj> + fill) nil) /)/ 

lu, + nw, = (ail + 6;^) cos jit^ 

in which the amplitude A of the free preccasiuti i» not involved. 

We have now to inquire into tho kind of information 
these diHgnuns uaii convey. (Jn i>iir plnn of nna]y(ii8, on thu hu» 
of adeflnite elaAttc Kartb on wliicli adiiittonal mativr can be d» 
placed, tbe lorcive necessary U> supply new an^'ulnr momentum u 
lUHt^rial that has cuiue into a position of ^reati-r dittmnl velod^ 
has to he aiipi'lied by tbis eartb, while it bos aho to euBtain tin 
ceutrifuyiil torce of tlil« material, Thf* oth«;r ways in which tbe 
mobile material renct« on tbe motion of tbe Kurth on which it il 
«npe^^n^sed are nBgligible in compiirison with these two.* 

For a lua^ m in uo-latitudo 6 the cenlrifitgal turqtia 
mflV^aiu^coe^ aronnd nn Bxiii at ri^ht anglee to tlio meridiau 
m. Tbe aggregate tnn^ue corresponding to its angular moaien 
in tta prsBent position is miir- sm 6 cr)» 9, as regards tbe equatoriil 
component which is In the meridian uf m. Tho former operates 
a whole aa a forcive, but only tbe tinie-grailient uf tbe latt«r thn 
acts, which is smllrvcits 26, where v is the velocity of m alo. 
meridian. Th« former pre pond«^ rates, in tbe ratio Jl>r 
therefore usually very much no, a*! ^Or i« of tbe order of 300 
per hour. On the oilier iiand, the centrifugal force of a new steady 
local load merely uiake^ the steady precoesicm occur nixmt a rtew 
axis uf inertia, ilius is not progreesive or cumulutive. This » 
n-fldily verihed by reversing the gmphical procedure; a steady 
Loixjiia, rf>presenteii by tbe end of a radius vector, becomea repi%- 
aeuted by an arc of a circle when refirred to axvi rotating witb 
t.be frve preeessional velocity, and thi.'« corresponds to a velocity 
of circular precession of tbe I'*ote wbilf? it la^ts. 

TbiA d<iubte uiodf, of action of traQs|>(>rled material, throuftli 
centrifugal force and through change of momentum of diurnal 
motion, renders interpretation of tbe torque-diagram to somi 
extent indefinite. 

Uiit, neglerting the rttect of change of intrinsic angular 
momentum, which, may be as much iis onc-tciith of the whole^ 
the torque will be^due Ui the cuntrifugiil forco of tlie 'listribatino 

' Tins is rcudilr seen by the I'rooeciiire of the note, p. 24, if wo iairodiifls 
the e«i-t foniiuk A,^ A'«, - E*, -?•»,+ !»,, where for sii additional ma«a m 
at xyt, ¥ = m^, S=iruez; wr are in fact merely neglecting n«, aotl A^ 
comiisred with OF*. 



I 



OT. 1906, Sfovemenl of the Earth's AxU of Rotation. 31 



the mobile load &t each ioataat^ and will \\im» indicate the 
geuerul fuatvires of Unit din Lri bat ion ; wliile lh« rat« of cbunK^ 
of the torque, i.e. the velocity in thi» torqiis-diagriiin, will 
give an imiiciktinii of the movemtint of the load. Tlio radius 
Teclor O P of the tor>]ue-<litt^ram at any iiisLivnt will imply a 
proportiuiml Hccimnilatioii of iiiulL-nalM in tuiudlc latitudes on 
the meridiHii at ri^lit an^lt'^ to O 1^ sn that atitipoJal tttciitimlatLoiis 
ruiuforce, but adjacent oi\^9, tiurth and south of the equator, coutJtcr- 
aet onch other. Tlie marked tendfiuey of the torque diagram (or 
the iteriod 1900-05 towards the side of the I'arific Ucean mia;ht 
thus hfi dufl to tiiinultaii(ioui4 accumulation of lond ikiL oti the aide 
of the Pacific, but iu the Dei^hlxxirhijod of tha perpendicular 
nievidiau. Thero is, howorer, n ]K>8«ib1o alternative to Iw kept in 
view, as followu. 

It has been suggested to ua by Professor Turni-r that the position 
of the oriiciii to which the curve of waiideriiig of the Pole of 
notation is referrtHl. i» subject to cousidtwblo iincertMinty. The 
observations and their rf^duction do not, however, seem to be at 
fault Hp(->dally in this dirt^ction ; unless tli*] unexplained coiiHtant 
(Kiinnra) term may be titken to indic-ate a ntdius of nncertainty 
due tu stuBonal instrumental channex. Thi» Ujrui, which recent 
discussiuii has confined to a smaller amplitude und to an annual 
period, was referred roufjValy to a displacement (mainly N and S) 
of the Earth's ceatre of (gravity : we have verified nlxive, hoitever, 
that no likely meridional tmntsfer due to seasonal change of 
leraperaluvB could produce an olfect sd ureat. 

There does not, in faot, seem to l>e any ground, apart from 
mere uncertainties, for taking the origin to whicli the wanderint^s 
of the Pole of rotation are referred to be othtr than a tixed point 
on the Knrth. Bat, on the other hand, this fix>.'d point muy liot 
be the Pole of inertia of the solid Earth. We can, however, make 
it so, by Heparstirig from tho solid Earth a tliin superficial sheet, 
and counting this with th*^ mobile itmterial. Tlie centrifuyal 
fnrrive due to this slK-et wdl then (vmstitnte a torque invarinble 
with respect to the Earth: and wa litive merely to suhLratl this 
iR>m the torquc-dianraui reft^rn^d to tlje Etirlh iu order lii obtain 
tliu torque due to the tooAe material alone. This sublnii-tioti of a 
constant vector term amounts simply to u change of origin. Thus 
on the final torque-diagram the origin is uncertain, and would 
naturally be placed in a-4 centml a position as possible. 

The proces.s. here carried out graphically may be compared with 
the procedure by succeBsive atepji as employed by Newcoinb, in 
which free precession occurs for an infinitesimal time U round an 
axis of inertia O Buppose<l tixed in the Earth, then O is moved on 
to O, as the result of the change of the mobile load during that 
lime, tiien fn-e precession takes placft round Oj for a time S/,, then 
Oj is moved on to 0« etc. Our method has virtually amounted to 
tho elimination of ttic free precessional motion, w t^itt 

angular velocity, thus leaving tho eausea which d' if 

inertia on the Earth's surface open to inspoctioi 






32 J'rof. Larmor and Major IlilU, Th* IrretpUar LXm. 

shirt of tbe axis of rotation iu ifNicd Ih^idk neglected for the 
Bpherieal Karib, iw in/ra. 

Iluw fur Uii> reaultt mny Uirow light on their eauaw il(^p«DiJ« 
Urgelv on a cani[Minsou of tlio tlia^runs with ibu dtapluieuienu 
of mailer on tlie Harlb's surface thit ar<! known to meteorology and 
oceiino;n-it|>ti,v. It may bo tUni not much cvrtnin information may 
ypt he di.Tivahl<i ; but, considering the long lime that obs«rvation« 
of the vandcrin}^ of the I'olo have bven accumulating, it can banlly 
b« aaid that it ii too toon to pre|Nirti for Uieir prcUmtnary diaeiiiiaoii 
from the geopfaynoal point of view. 

The niod<T of reduction on which this popcr iii found«d givw ■ 
force diagram which exbihiu the tonjne ansMined bjr the reat of tb« 
Kartb owing to the diaplacoment iu and over it of the movable 
tnaiim treated aa independent bodiea It remains valid, however 
mpid the free preoeadon may )>l>. In the cum of the nctna) eartfa 
the Ult«r is aluw, tMriug ('/(C-A) iiiilercat days, in wliich the 
difference of momonla of inertlu hna ita effective or dynamical 
value, tlinii lengthemn.,' the free period from 306 to 438 solar daya. 
Iu this cMae variotu fvaturea nj>5ume simple formic, as appears in tho 
Foineot repreaeDtaliuD by a rolling eUipHjnd. When this ellipeoid 
b very nearly spherical, the nxi« of mtatiitn, drawn from ita fixed 
centre to the point of contact with the plane on whicit it rolls, ia 
at u umatl inclination to the iuvariable dirvclion of renultant 
motneiituni (whirh is noruul to thai plane) coni|>are'l wiili iu 
incUnaliun to the axi« nf inertia; thus the axis of rotal-ion b 
praetieally fixed in direction in s|mc«— HiXL-ept na regftrda the 
anpcrpoaed Inni-aolar prcnuaioii. When the ellipeoid of inertia bfl 
nearly of revolution, as in the cus« uf the Earth, the )iole of inertia V 
lhu4 rvroUea in i*psce vrith the unifomi free pree«Mioiial velocity, 
around thu lixixl dirrotiou of the pulf of rutation, while at the name 
time it is nnUcrgoing such shifts an the riMltstribution of matorial 
geometrically ro(|uirea Our p^>codnn; in th<> aUivo has been to^ 
eliun'tiaie ihi* uniform pr«cf«»i'>it, and tb<^ residue i» a ^^ap)li■I^H 
rnprtMeutulioii of the irregnUr Hhifta. nr rather of the torques which 
pro<luce them. 



Tlie diM>u8sl(in of theqncation whether in |ia>t geological history 
llin pole of rntation Iihb wandered extensively in tlic Earth Mwma 
also ca|>able of IteiuK boM-d on tiiiiiiile graphic repipjwntation. 
ahsll assume, as before, that the dyriiimicK uf the Kurtli's rotation 
based it each instant an a nimplo kinetic energ}' T given hy 

2T •■ Aw,« + B«D,» + C«,«, 

where A. It, C are efTcctivu moments of inertia ; it follows that the 
angular mumi-ntnm (I., M, N) i* ;;iven by the fumiula 



itory 
temafl 

larafl 



Darintt the history ul the Esrth (I^ M, N), resultant G, must Iw 
remained conatunt, while T will probably have diminished throagh 



J 




w 



Nov. 1906. Movement of tht. Harih's Axis of Rotation. 33 

frictional agoaoy. Abstraction is Lere made of the sular and luoar 
forced preceuions, vbich compciiBiile the torque uf oxlraDeDOs 
attnctioiu without affe^itin^ the poRiiton nf the axiH of rotation in 
tbo Earth. Tli« free motion i» represcDttd, after Poiusot, by the 
Bogutar motion of a moniental ellipsuid, say 

'fbo direction of the axta of instsntaneom rotutioQ intersects its 
surface at the point {xyz) such that 

K 



-^=i^ = ^, therefore = (^4)' 

U»] Wj »Uj \»T/ 




i. 



The distance p of the tangent plane at this point {xyt) from the 
centre is given by 

~3KT 

Thus if K~^»2T, we have pisQ~^ = constant ; this tangent plane 
is then Kxed as regards distance fnnu the centre, a^ well as rei;ards 
\XA direction, which is perpeudiculai- to the invariable momeutam 
(U Mt ^)' Thus it is entirely iixed. 

Tlitis the free precessional raolion of the sluwly changing EarUi 
is represented by the vurying ellipsoid 

railing with centre fixed, so as to keep in contact with this tixed 
plane vrhose tliataiice from tho cnntrH \ti Q '. 

If the kinvtic energy keeps coiiBtant, this is simply Poinsot's 
reprvsoutation. The axin i)f rutHtiun will circulate in the body 
around the axis i>f greiitesi moment of iDertin, atui in spac^ around 
the axis of result-mii angular niDinentuiu. The amplitude of this 
free prece^siiin will be kept sntall by internal friction, so that the 
axis of rotation will always he near the pri]icipFilaxi<!i, and can never 
wander further from its original pusition than the latter dues. It 
will reiiuire a good deal of change of distribution of mass to move 
this principal axi« very far; to muve it into the equator the 
nulios nf the Kartb mubt shrink to the order of 40 miles alotig the 
equator near the new Poles, and expand to about au equal extent 
near the ohgitial Pule». 

If the l!^rth in slirinkin^ uniformly, the moments of inertia vary 
as Pj where / represents linear diciiensions ; thus the angular 
velocitiee vary as ("' and the kinotic; energy varies as i~'. Thus 
the dimensions of this rtilling ellipsoid remain unalten^d. The 
distance of the plane on wliiob it rolls al^o keeps fixed. Honca 
nniform shrinkage without frictional loss of energy would not atfect 
the amplitude of the free precession, or cau»e the Poles \o taV^nLtft. 



34 



Mr EdtHngioH, Tht St/gtematie 



LXVIL I 



Dimiimtiiiii of tlie euerfty of rotation throngh internal frictin^ 
without change of (A, B, C), would increase the dimensions ol 
roUing dlipsolii (m the proportion of T"'), atid so would 
strongly for etahilit}- of the axis of rotation, an above rematkii 
Sttch increase can only proceed to a liniitefl extent, determined h 
the ellipsoid just failing to intcKe^jt, iitid so touching the fiu 
planu at thtt u\tn>mity of it»i axis. 

A discuasioii of the geological prohlenk of displacement of fi 
polar axit« in the Earth munb take Hccouut of considemtions audi 
these. 



The SytUematic- Motions of tka Start. 
By A- S Kddington, RA., M.Sc 

I. Inh-odmtion 



EOf late years astrouoniers who have investigated the prop 
raotluDS of iiUiri} have heen inaiuly intorejitifd in delcitnining 
^direction of the solar mation. It is usual to assume that, if m 
pDnsider a suttlciont number nf (tiara, their true niotions will be 
T&ndoni ; on this asauniption the dirpction of the sun's motion hi 
been cHlculKtwd. 

ProfessLir J. i_'. Kapteyn * ha;^ exninincd the Bradley propi 
motions to find nut whether this assumption is approximately tree 
He concludes that it is incorr^t. Relative to the suu, he fiixli 
two "favoured" directions of itiotinn jiiKtead of one. Xuplep 
HaggesteJ that there aru two systenm or "drifts" of stars; the* 
two ilrifts an- in motion relative tn one another. If the whc4t 
universe forniR one system (or one chaos) we can opeok of iti 
motion rclntive t^i th^ sun ; hut it is mnrc natural, though |>erhA|ri 
misleading, to speak of tht nim's motion rehtttve to it. But il 
there are two systems, we may as well dn)p the idea of the so 
motion altogether, and ^peak of the niotiuns of the two dri 
relative to the sun. 

In thii paper I have attempted to aubject Kapteyn'n theory 
a quantitative test by examining the Green wJcb-Groomb 
proper motions. I *viis k-d to undertake this by the followi 
considemtions :— 

(i) The importance and revolutionary character of Kapbe 
discovery render independent cnnfirmatiou very desirable. 

(2) The Greeuwicli-fTroonibridgo proper motions, recen 
determined by Dyaon and Thackeray, affdrd new mati>rial for 
purpose. I had the advantage of acc^es^ to Hyson and Thacken 
calcid^itions used in their detemii nation of the so-ealted aulur a 

(3) The Bradley stara arc all bright »tars. The Groooibni 
cataloguu includes n large pro]>oi'tion nf stars betwucn the sevei 
and ninth magnitudes ; it is desirable to find out whether 
fall into Kapteyn's two drifts. 

* Brii. AwK. Report, 1905. 




^ 
^ 



Nov, 1906. 



MolioM of the Stars. 



35 



I 



» 



(4) The Critiombridge stars number about 4500 nnd ar« all 
within 52' of tbe north |M>le. 'llie 2500 Uradley Rtare cover moat 
of the Nky. For some purposes there is uu advantage in comparing 
the pheiioitieiiu in ditTereiil parts of the sky, hut for quantitative 
test* of thfi theiiry 1 liuve found d(^n«tty of distribution essential ; 
this the (irofimhridge rHtnlngiie affords. 

I have also examined iu the same manner thu Greenn-ich- 
Carriiigton proper luotious. 

When more determinations of liuB-of-sight velocitie* are 
published, [lerhaps a oompletc demonstration of the two-drift 
theory will be possibW. What ia hure attempted ia to ^ow that 
there exist anoumlics of a rc-markubit: and syBtt^malic character in . 
tbe proper motions (or what are beliovwi to ho thf proper motions) 
of the AtarK ; and that theite anomalies are, so far as our evidnnce 
goes, entirely explainsd if we suppose the visible universe to 
consiat in the main of two t^treams of stars crossing thrr>iigh one 
another. 

The t**t of a hypothesis is its power of predicting fucts. It 
is easy to pick out halfn-dozen stars which, our theory predicts^ 
ivill havH Hu avi-rago velocity towanLn the sun, and another half- 
dozen from the same part uf the sky which will havo a velocity 
away from the aun. 

Until some such simple test is applied, it would be wrong to 
regard the theory as established. On the nthei' htind. it muHt not 
be forgotten that, should the two-drift theory fuil whu-u tho crucial 
teat Is applied, some other oxplatiation will hove to be found for 
tbe remarkable phenomena to wliich Kapteyti (ins called attention. 

2. MathKmatictti 'iliewy. 

I deliiie a " drift of stars " to be a systoui of stars whoae 
velocities relative to some system of axes are quit^* haphazard. 
The velocity of the drift is thu v«locity uf ihe aforesaiil system of 
axea. _The " peculiar" velocity of :» star is its velocity relative to 
that system. For example, the orilinary hypothesis <jn which 
diacusaiona of the solar motion are bused rt^gardii the universe as 
forming one such drift, tt is sometimes further assumed that this 
drift is at absolute rust ; but. of ctmrse, referred to the i*un, it Is in 
relative motion. 

] shall accept, a^ the best inaCbematical equivalent of 
"haphuard," a distribution of %'clucittes according to Maxwell's 
law. Of course there is no analogy betwcou tlio causes which 
determine tbe velocities of the molecules of a gas And those of the 
atari. In the former cusa it is the collisions which make the 
inoleculus obey this Itiw. But Jvuns ' has uhowii that of all 
distributions luwiiuj Me mme nwyrgy, tbut jtcconling to Maxwell's 
law is the most probable; and as i\m number of bodieei increase^, 
(he probability of a Maxwellian distribution approaches certainty. 

• The Di/niitnKai Th^iy of Oajtt. | 56. We take »■• our bitxit 0/ 
pnbabilittt iliat till raluoa of b relodty <:onipouMit src eqiu'ly ^^toNaXiVv. 



Mr Eddin^Uni. Th€ SywUmalic 




LXVH. I, 



For our purpuncK it will be suftioieiil lo uccepc tbe Maxwcllwii 
(tistribiition a» a Klaniard ; and it will be tbe object of the eom- 
pariaoD of obeerratioti and theory to discover any iu*rk«d davjataoiia 
from tbl« fitaailard distribution of stellar Tetocitiee. 

OoQstder a small r«gioD of the sky which cao be coDaidMed 
approximatAly plane, and aoppoee tbe itt&re in it belong to one 
drift We aliatl cotuider tbetr linear velocitiea, but ignura noUon 
ill the line of nuhu 

Let ihe ilrift velocity bp V along Or, ami let tbe number of 
■Lira having com|>onenc [teculiar vdiicities between (u, r) ami 
{n+du, r + <^) be in aceortlance vUh Maxwell's law 

Ae-^^^^dudv 

I aball call h tbe drift-coaatant ; it is ooQMCtad with die 
mean peculiar speed ti of the stara of the drift by tbe ratatloa 



"-^/^^ 



If r b« the resultant vcluoity, B ita inclination to Oie, we vbatl 
have 

»9^B8-r*-(.Vt-aVrcM« 
dwivmrdrdS 

Hence the number of itara having proper motions in dirertinns 
incliuod to Ox between 6 and $ + dS 



or patthig f » r - V ooa ^, 



M*'-»'"«^*r* **U + Vco«tf)A 

■' -VoMf 



now put A: « X and AV oos •• r the number beoomas 
-^-•«w{r-J*t--^x + r)dx} 



MO 



mhvn B is ind»p«Ddint of $. 

The above function of r ia very important in 
Table T. gives the values of lof(/(r). where 



rhat follows. 



Ar).j^{i.^j-y-.u} 



Nov. 1906. 



Motimis of (he Stars. 



37 



Tablk I. 



T. 


IOg/(T). 


T. 


' Io«/(r). 

1 


T. 


IOg/(r). 


1 ,. 
1 


10g/(TX i 


-1-3 


3-997 


-■4 


1-471 


*5 


0'i88 


• 

1*3 


1152 


-1-2 


i'041 


-■3 


■536 


-6 


-288 


1-4 


■300 


- 1-1 


■087 


- '2 


•605 


7 


■395 


1*5 


•455 


- i-o 


•135 


-•I 


-676 


-8 


■506 


1-6 


-618 


- -9 


■185 





: 75 » 


•9 


- -623 


17 


787 


- -8 


•238 


•I 


•830 


i-o 


746 


1-8 


■964 


- 7 


'292 


■2 


1 '913 


i-i 


-875 


1-9 


2-148 


- -6 


•349 


•3 


O'OOO 


1*2 


I -010 


2-0 


■339 


- '5 


•409 


•4 


, -091 











Congider tJie curve obtained by dratoing the radiue vector in 
any direction proportional to the number of stars liaving proper 
motions in iliat direction. 

The polar equation of the curve will of course be r x / (ft V cob 6), 



KV-w 




hV-.o 




hV-04 



hv-.9 




Fia. I. 



38 



Mr Eddingtofi, Tke StfattmtUie 



or more ^nerallj, if the drift ia in thn directioD 0„ instead uf being 
along the initiul Utie, 

Thu shape of tlie curve dv^ii>.ls oo tho parainetor AV ; in other 
words, it depend* on the rnliu of tho drift Telocity tri the 
peculiar veloritv. It doe< not in any way depend on the di«tancea 
of the slant. 

Fig. 1 shows thp cur**B« drawn for (our ditft-ronl value* of fcV, 
It will bo noticed how rapidly the abape of the curve ehaagw for 
■mall variationn in AV. 




3. Treatment 0/ the Ofmntti Propa- Motioiu. 

Tho n^on uovored by the (}roombridgi! cutalopic compriMt 
that part of the sky within 51* of the ni>nh |)olr. I divided ic 
tuto Bcven regions aa follows : — 



B«l|iaoA 


M.P.D. o* 


-M>' 




.. B 


v.r.i\ »• 


-S'" 


R.A.sx^ai> 


,. c 


,, 




.. 3*-6» 


« D 


,, 




.. 6h-l0* 


,. K 


,, 




.. Iofc-14* 


., f 


ti 




H ■4*-l8'' 


.. G 


•1 




„ l8»<-««' 



In making thia diviaion il wati nec8«Hr)- to steer between t« 
evUa. If too large a tuKion ia cboaua, (be proper motiooa will m 
follow the same law at all |iarta of it, and thuy cannot fairly ha 
tnatad as all in one plane. But the refriona mu«t be lir^ enough 
to Dontain a xufticient number of atara ; it ia dilficnlt to deal 
mAthumattcidly with a region contaiuin); lea» than 400 Htara. 

lu diacuuing vmt of these Rgi'Uia. n lablo waa fint mad* 
ihowiug how many stars tr*< nioviDg in each direction. The angle 
9 which indicntvM the direction wu meaiured in a cuaular-clockwtas 
direction (aa .ven in the nky) from the direction of increaaing R.A. 
at the centre of the region.* Thus 6»go* would mean towaida 
the equator and parallel to tho oeiitnl mvrnlinn. 

Fig. a «howa curvns drawn to rcprfweut thcae tablea Aa in 
th« tbei'ratical cnrvea of fig. 1, the radiua vector in any direction 
ia pruportional to thu anmbcr of itam whoae proper motion* am ia 
that direelion. 

Let ua consider, for example, the ourve B (oorresuonding to 
region B), and eompArv it with the theoretical eingle drift curvea 
of fig. 1. Perhapa the looal remarkable feature isi the rxtmordinary 
minimnm between oa and oh, TLe iniinber of »iari having 
direotiona nf mntion within this right angle i« fonnd nu referenc* 
to the table to bo only 63 one uf S6i. Hnt the curve dilTen 

* In the taw ot regioa A. tli« diMCtoa *»o* b aloac the mvridtaa », 



40 



Mr Eddingtwi, The SyUenuUic 




'oases of P and K. In region A vo hsve two maxima of the 

vector nearly oppoxite ono unotiier, so thai the diaa^eemetit 
tbec^ry iH in some rriipL-cts more rumnrkablc still. K.>Lpt«yD la 
iuvoati^tion fmmd this name iliaHgreetncnt, and pointed oot 
explauacioii — tbnt there are really two drifts of atara. 

I have accordingij analysed each region scparutely to sea 
can be accouiiUid tor ou the a^umpticiti ihat each curvo ic < 
pounded of two eimpld drift curves For instance, in fig. 3, X 
T are theoretical curves for single driftti ; X represents a drift 1 




Vlii. 3. 




>ii;. 4. 



taining 41 S stars, und for which AV= 1*55 ; Y a drifi contaii 
430 Btars, and for which AV = -45. The directions of niotton of' 
two driftfi aio inclined at an &\\^\n nf 120*. Tlie cnnipound cH 
Z is drawn with its rndius rector in any direction equal to 
sum of the radii vectorc^s of X and Y in that direction. It thi 
fore corresponds to a mixture of the stars of the two drifts ab 
mentioned. The curve Z is the best approximation tn fig. 2B wl| 
1 am able to obtain by combining two simple ctirves, Fi« 
shows a companion of the two. Thcr» is a sniall ditTi^rence ia 
two curves between the radii $^^0'' and 80*, amounting to 





fov. 1906. 



Motions of the Stars. 



4' 



ctiiw of 2^ iiUrK altogether {i.e. the obfierved ciirvA Xxoa 1 14 ntan, 
ere the thecretical curve has go Rtara). Elaevrhere the agree- 
'^menc va practically perfect. For this und thn other ri^^ions, t!ie 
jAgreeuieut is better see-n by referring to the tablet* which follow, 
d Mptjcially to fig«. 5 and 6. 
Ill Tables II. to VII., corrK«poadinK U> rariooB values of 6, the 
fth rohimn ithowK lite actual inttriher of »tsra Imviiig pnjper 

^otioiig in that direction* — the radius vector of the diaKrama. 

lie fourtli coluoin ebows bbt? theoretical number given by my 
alytiis, and the second und third columtts siiow how the two 
rift4 cootribiite to this theorniical mimlmr. The compariBon of 
e ob>>erved and theoretical numbers is shown in fi|^. 5 and 6 for 
Dur regions. Tlie number uf i^tiire and the cor respond itig direction 
if motiuu 6 are plotted as ordinate and absuiesa instead of (as in the 
'ftvions diagrams) as polar co-onlinatea. 

It mu»t nut be jtuppoaed that I claim that two drifts represent 
m^iletely the pheuomenu of the ilistributLon of proper moUons, 
d thnt the discordances are uoccsMarily cither errors of olj«^va- 
Ion or the purely accidental depttrturce which the theory of 
irobahility allows. Local irregularities must he expected ; perhaps 
third smaller drift exists throughout the sky, or one of the two 
Tincipal drift*! may prove to be cumpouud. What \& claimed for 
he two-<1rift hyp»the8iB is that it is a good fir»t approxiuiatioD, 
irheroas the one-drift hypothesiit is nn approximation at all. 

VAcih region has been analysed without reference to the others. 
The six disposable constants of each theoretical cvirve have been 
letetniiufd by trial and error, so as to make it coincide as nearly 
possible with the observed curve. Of course, if the same two 
irifts persist from region to region, there must be relations between 
bft coastants of the drifls in the diffurcDt regions. The fulfilment 
these relations is a good tent of the thecny. 

' More prmiMly— ntifi-tkinl t\w uumbcr of Btnre liiivintf pruper muliaiix 
dirwtioDs botvMu 9 - 15' sud 9+ ij*. The other thrse eolanms huve teen 
' tmoothffd " in the sua* wsy. 



42 



Mr SdeUngton, The Sydemattc 



LXTILI 



Tabus II.— Rboion A. 



DhectloD A. 




CftJonUted. 




Obaenwd, 


oalettlalift. 




IMni. 


IMttlt 


TotiJ. ^ 


5" 


4a 


5 


47 


*■ 

49 


+ 3 


'5* 


35 


S 


40 


39 


-1 


ar 


36 


5 


3« 


27 


-4 


35' 


i& 


5 


21 


30 


-I 


45" 


9 


6 


15 


iS 


+ 3 


ss* 


5 


7 


la 


*5 


+ 3 


6j- 


3 


S 


ID 


14 


+ 4 


75° 


I 


8 


9 


13 


+ 3 


ss" 


I 


9 


10 


T2 


+ 3 


95" 


r 


10 


II 


11 


D 


los" 





ti 


II 


10 


-1 


US' 





12 


iz 


10 


- a 


"5' 





12 


13 


9 


-3 


135' 





13 


13 


13 





^45* 





IJ 


'3 


11 


-3 


»55° 





13 


13 


14 


+ 1 


165- 


o 


»3 


13 


la 


- 1 


175' 





13 


13 


14 


+ 1 


isr 





12 


13 


[2 





195' 


o 


12 


13 


'3 


+ 1 


205" 





11 


II 


11 





215' 





ID 


lO 


10 





235" 





9 


9 


7 


— X 


235° 





& 


a 


7 


- 1 


245' 





S 


a 


9 


+ 1 


ass* 


p 


7 


7 


9 


+ 3 


265- 


I 


6 


7 


7 





375' 


r 


5 


6 


7 


+ I 


285- 


1 


5 


6 


9 


+ 3 


295° 


z 


5 


7 


ir 


+ 4 


305' 


5 


5 


10 


IZ 


+ Z 


315° 


9 


5 


14 


15 


+ 1 


325' 


IS 


4 


20 


31 


+ 1 


335* 


36 


4 


30 


29 


- I 


345' 


35 


4 


39 


39 


a 


355' 


+2 


5 


47 


47 





' ToUltt . 


276 


393 


569 


585 





av. 1906. 


™ 


Motions of the Stars. 


4$ ^ 


' 


Tablk III.- 


-BaoiOK B. 




■ 


1 

PlfMttmi*. 
5' 


CKtcaJktMt. 


OtaMTvad. 


Dlirar«M* 
oliMrvcd— 
ealonlOcd. 


3 


' iMftr 

59 


&rlftlt 


Total. 
65 


6 


67 


+ X 


'5' 


59 


7 


66 


65 


-1 


^H 


25° 


SI 


8 


59 


54 


5 


^^H 


J5' 


3R 


9 


47 


47 





^^1 


45° 


25 


10 


35 


37 


1 3 


^^1 


55° 


»S 


12 


27 


31 


4-4 


^^1 


65* 


8 


14 


2a 


30 


+8 


^H 


75' 


5 


16 


at 


38 


+ 7 


^^1 


ay 


2 


18 


20 


as 


+ 5 


^H 


95' 




30 


21 


i9 


-2 


^^1 


'OS' 




22 


*3 


so 


-3 


^H 


"S 




33 


24 


20 


-4 


^^^Hi 


las-^ 




34 


as 


a6 


t 1 


^^1 


'35' 




H 


»S 


as 





^H 


US" 





33 


as 


a6 


+ 3 


^H 


m"^ 





U 


33 


32 





^^1 


165- 





30 


30 


ao 





^H 


'75' 





18 


iS 


18 





^^1 


l»i" 





16 


16 


18 


+a 


^H 


195'' 





14 


■4 


IS 


+ 1 


^H 


aos* 





13 


13 


16 


t-4 


^^1 


«'S' 





10 


10 


10 





^^1' 


235" 





9 


9 


5 


-4 


^H. 


235' 





S 


8 


7 


- 1 


^^1 


^45' 


> 


7 


8 


6 


-3 


^^1 


255' 


1 


6 


7 


6 


- I 


^^^Hi 


36s' 


I 


6 


7 


7 





^H' 


^75' 


I 


5 


6 


6 





^^^M\ 


»S5' 


I 


S 


6 


8 


■fa 


^^H 


»95* 


2 


5 


7 


8 


+ 1 


^H 


y>s' 


5 


S 


10 


ID 





^^B 


315' 


8 


5 


13 


'3 


_l 


3»S' 


15 


5 


ao 


18 


^ 


335' 


as 


S 


30 


a7 


■ 


345" 


38 


5 


43 


43 


■ 


3SS- 


5' 


6 


57 


A^ 


5 


TolhU . 


4.6 


430 


84f 


^ 










i 



44 


Mr Eddim.gUm, 


The HysUnuUic 


LXTEl 


< 


Tablb IV.- 


-Region C. 




Direction*. 


CalculAted. 


ObMTTSd. 


DUTwiyi 

CBlcltlltWl 


' Drittl. 


DiUtll. 


ToUl. 


5° 


5 


6 


11 


II 





15° 


9 


7 


16 


IS 


- I 


25° 


16 


7 


23 


24 


+ 1 


35" 


24 


8 


32 


34 


+ 2 


45° 


33 


9 


41 


4a 


+ 1 


55* 


35 


9 


44 


43 


-I 


65' 


32 


10 


42 


38 


-4 


75° 


24 


II 


35 


35 





85° 
95° 


16 
9 


12 
13 


28 
22 


27 
23 


-I 
+ 1 


105° 


5 


13 


18 


16 


-2 


115' 


2 


14 


16 


14 


-2 


125- 


I 


14 


15 


12 


-3 


135° 


I 


14 


15 


13 


-2 


145° 


I 


»3 


14 


14 





155' 





13 


13 


14 


+ 1 


.65' 





12 


12 


12 





»75° 





II 


II 


II 





185° 





10 


10 


10 





195° 





9 


9 


10 


+ 1 


205° 





9 


9 


9 





215" 





8 


8 


8 





225° 





7 


7 


7 





235° 





7 


7 


6 


-I 


245- 





6 


6 


6 





255° 





6 


6 


4 


- 2 


265' 





5 


5 


4 


- I 


275' 





5 


5 


4 


- I 


285" 





5 


5 


5 





295° 





5 


5 


5 





305° 





5 


5 


6 


+ 1 


3*5° 





5 


5 


7 


+ 2 


325' 


t 


5 


6 


7 


+ 1 


335' 


I 


5 


6 


6 





345° 


1 


5 


6 


6 





355'" 


2 


6 


8 


8 





Totals 


217 


309 


526 


516 





3V. 1906. 



Motions of the Stars. 



45 



Tabu V.— Ruiok D. 



Mreotlon t. 


CUcaUted. 


Obaerrod. 


Dtfforaioe 
obwrwd— 

cslouUted. 


' DrtftL 


Drift U. 


TotaL 


5' 





5 


5 


4 


-1 


IS' 





5 


5 


S 





25° 




5 


6 


5 


- I 


35* 




5 


6 


7 


-1 


45" 




5 


6 


8 


+ 2 


55" 




5 


7 


9 


+ 2 


65" 




5 


9 


12 


+ 3 


75° 


6 


6 


12 


12 





85' 


10 


6 


16 


16 





95° 


16 


6 


22 


ao 


-2 


105' 


22 


6 


28 


30 


+ 2 


115' 


27 


7 


34 


35 


+ 1 


125' 


29 


7 


36 


37 


+ 1 


'35° 


37 


7 


34 


30 


-4 


145' 


22 


7 


29 


27 


-2 


155" 


16 


8 


24 


22 


-2 


165- 


10 


8 


18 


>9 


+ 1 


'75° 


6 


8 


14 


16 


+ 2 


185° 


4 


8 


12 


15 


+ 3 


'95' 


2 


8 


10 


15 


+ 5 


aos" 


1 


8 


9 


10 


+ 1 


215" 


1 


8 


9 


8 


- 1 


225' 


I 


7 


8 


6 


-2 


235° 


R 


7 


7 


7 





245° 





7 


7 


8 


+ 1 


255° 





7 


7 


8 


+ 1 


265° 





6 


6 


6 





275° 





6 


6 


5 


- 1 


285° 





6 


6 


5 


- r 


295" 





6 


6 


5 


- I 


305° 









5 





315" 









5 





325° 









5 





335° 









5 





345° 









6 


+ I 


355° 









5 





Total H 


209 


225 


434 


443 





46 



Mr JUddingUm, The Syetematie 



LXm! 



Table VI.— Rboioh F. 



DinoUon*. 

5° 




Oklotdatod. 




ObMmd. 


olMcrrei- 

ralgnlitot 


' Drift I. 


Drift n. 


Toul. ^ 





6 


6 


4 


-2 


15° 





7 


7 


5 


-2 


25" 





8 


8 


6 


-2 


35" 





10 


10 


9 


-1 


; 45" 





II 


11 


10 


- I 


1 ^5' 





12 


12 


14 


+ 2 


65" 





■' 


12 


M 


+ 2 


1 75' 





•3 


»3 


M 


+ 1 


' 85- 





13 


'3 


'3 





95° 





12 


12 


12 





105" 


1 


.2 


13 


10 


-3 


115' 


I 


11 


12 


II 


- 1 


125' 


I 


10 


II 


10 


- 1 


■35- 


I 


8 


9 


10 


+ 1 


M5' 


2 


7 


9 


7 1 


-2 


15s' 


3 


6 


9 


9 1 





165" 


5 


6 


II 


9 t 


-2 


175° 


7 


5 


12 


^* 1 


+ 2 


185- 


II 


4 


15 


M 1 


-I 


>95° 


15 


4 


'9 


16 1 


-3 


205° 


19 


3 


22 


21 1 


- I 


215° 


23 


3 


26 


27 ■' 


+ 1 


225" 


24 


J 


27 


29 


+ 2 


'35° 


23 


3 


26 


2« 





245° 


19 


3 


22 


19 


- 3 


255° 


>5 


3 


18 


17 


- I 


265= 


II 


3 


14 


12 


-2 


275° 


7 


3 


10 


11 


+ I 


285- 


5 


3 


8 


II 


+ 3 


295° 


3 


3 


6 


s 


+ 2 


3"5" 


2 


3 


5 


7 


+ 2 


315" 


I 


3 


4 


6 


+ 2 


325° 


I 


4 


5 


6 : 


+ I 


335" 


• 


4 


5 


5 





345° 


1 


5 1 


6 


5 


-I 


355° 





6 1 


6 


' 1 


- 2 


Totals . 


202 


232 


434 


425 





rv. 1906. 


r 


MotioHS qfthe Stars. 


1 






Xablk VIL— ItKiiox a. , 




■ 


^ 




OiJeuiAt«d. 




OUrenra 


^H 


Mm'Utrn 8, 






OhMrred. 


obMrrved'— 




' Drtltl. 


Itrltt II. 


Total. 


^H 


■ 












^^^H 


5' 


36 


9 


35 


39 


+ 4 


^H 


•5" 


32 


" 


ii 


39 


+ 6 


^^1 


as' 




IZ 


29 


34 


+ 5 


^^1 


J5 




14 


*7 


28 


+ 1 


^^1 


45' 




iti 


27 


27 





^^1 


55" 




18 


36 


28 


+ 2 


^^1 


65" 




21 


iS 


y> 


+ 2 


^H 


75" 




24 


29 


20 


a 


^^1 


ss' 




26 


5" 


3' 





^^B 


95* 




29 


3.1 


34 


1 1 


^^1 


lOf 




io 


3J 


33 





^^1 


US' 




3> 


34 


32 


-a 


^^1 


IIS" 




31 


34 


34 


a 


^^1 


>35' 




S*" 


5.1 


35 


4- 2 


^^1 


US' 




29 


32 


Si 


f 1 


^^1 


155" 




36 


29 


27 


- 2 


^^1 


165- 




M 


27 


2S 


-t I 


^H 


ns' 




21 


»4 


27 


+ 3 


^^1 


18s' 




j8 


21 


24 


+ 3 


^1 


'95' 




16 


20 


23 


+ 2 


^^M 


aoj- 




14 


■9 


30 


+ 1 


^^M 


«I5' 




12 


'7 


20 


+ 3 


^^H 


MS' 




II 


t8 


17 


- 1 


^^1 


^35" 




9 


17 


18 


n 


^^H 


*45* 


tl 


8 


19 


»9 


& 


^^P 


SSS* 


13 


» 


31 


ao 


- 1 


^^M 


a6s- 


17 


7 


24 


35 


+ 1 


^^M 


>7S" 


13 


7 


29 


39 





^^H 


*8r 


a6 


6 


32 


32 


- D 


^^1 


m' 


3» 


6 38 


34 


-4 «^ 


^k^H 


305' 


36 


6 


42 


38 


'^M 


^K^KI 


3»5' 


40 


6 


46 


46 


,^^ 


^^^BH 


3a5" 


41 


7 


4.S 


4S 




^^H 


335' 


40 


7 


4" .:6 


. 


^^H 


34J* 


36 


8 


-J ! 


> 


▲^1 


35S' 


j2 


S 


4 


* I 




TouIh 


J30 


566 


\< • 




■ 


^^ 


^^ 


- 


^- 


--— 


K.^1 



48 



Mr Eddingtwi, The SystemcUic 



Lxvr 




•„OI J8(i Sltt|B JO -O^ 




50 Mr Bddx%\gion, The SjfMematic 



4. lirmilU qf the Anaijfris, 

Tbe followiiij: aro tlw cocuuuls of t)i<> drift« in the Mrml 
tons. Thvy aro tbe valam on which tbe culuuui bct Ud 
'colonlAtrd " ill tliQ |>r«oedin({ lablei iirv hwed. 

Tablk VI I r. 



Orini. 



MftU. 



INniabtr oTitui . 
AV . 

I Mnmbtr i4 itcn . 
StgfARB AV . . . 



Region V 



N»mUTo(«t«n . 

AV . . . 

«. ■ ■ - 



I Numl'H or hl«r* . 
Rwoa li - AV . 

k . - - 

1Xnmb*r nt Ktin . 
AV 

KiinibR' of rUit , 
S^hmO (AV . 



(Kii 



177 




4IK 

'■5? 
10 


4J0 
45 

130- 


ai7 
55 


3P9 


1-40 


»*5 


aoa 

125' 


*3a 


520 

75 


5*6 
■45 

120* 



Region E conuiued too few atan lo wialyM MttBfaetorQy. 

Usjng a glol)e, 1 entnml the din'ctiun« of tbe driftv as great 
circle* on it. The greet cirde* wero drawn from tbe umtm of 
regjrinii {whinh tn the mm of regioM IICDG wen uannwd to be 
nt N.P.U. 40**) iti lbi> directionfi iiKlicuted by 0^ in tbe abov« 
rtwulbN. SuppleQivnlint; the drswiuj; hy '.kIc illation, I found that 
(or drift I. tho ^rrat ctrcles (iiroducpd Iwckwords) til ptmiMd cUma 
to Utt \rnul iLA. itt**, DrcL +tSi*. The occumcy wm mtbar 
eurpriiiing : Hre (-ircl(>« [m'^iwd witbm 3* of the |>oint ; tbst for 
region O wu alwiit 5' I'ut. T'jc *tAn of drift I. h«ve rieartjr e 
ODBtnton veK)Ctl; rrlittire to the «un ewaj from thri point. ) 
dull call tho point (^,. In spite of the cloee itgrecairni of tbe 
greet circlee, tbej int«ricct et eo acute an angle, all coniinK from 

* TfaU wai vvntlMl liv *(.-tUAl oa]<'uUlii>a of lh« centre af ni<«n p-i«itioD of 
tlie itan in wvaiBl rt^krion*. K«r ¥ itio rrDtn> viik ukeD to Iw X.r D j6'; 
it 99ti >\imcor«tt^ th«l iMiiic ilan botvotn o* tinl 20' N. !'.(>. Iis/l 'K-i't-laatAnr 
Ifwii l»<^:u<li*l lu tl<<> i<-jp.)ii. A* lb* iitiml«' of «un tn tvctou F wouUt liatt 
bMD too few to atulyot if iliej v«« nebHlfd, th* iMulu for thu »ii|[iu«atoil 

in hav* tr»ii ntaliiMt, 



Xov. igo6. 



^fotio1^s of th^ Stars. 



a limited region of the eky, that ij^ is not very accurately deter- 
niined. especially aa re^anlff iledinatiun. 

Tbeorelically, /iV sliotild be proportional to tbi* Hiti<> nf the 
uif(ular distaticfl of the urea fram Qj, lor V ia tb« component 
tfclociiy of tht' drift aeros* the linf of stijht. Tlie fullowinjj table 
shows a companion lietween obflervfttion an'i theory. TTie deereaM 
in AV aK we approach Q^ is iudicattid, but the >igreemenl is only 
rough. In particular, region G shows touch too guiall a value. 



Bcfiott. 


Dbt. Iroin <h- 


Sin* of DIrUdm. 


hW. 


A 


7a* 


■95 


1-65 


B 


76- 


•97 


»*5S 


C 


lor" 


•96 


'■65 


D 


I07- 


•96 


1-40 


S 


43' 


•68 


I'ao 


G 


4©^ 


•64 


75 



Examining the rcBulta for drift II. in the aaue way, we must 
b«ir ill mind tint the same dct*ree of accuracy is not to be ex- 
pected. The drift II. f^iirveni are not very elongated, and we cannot 
telt with preciiiion which way they are pointing, [f we lake the 
velocity oF thu nun relutivu Ui ilrifl I. t<> lie iS kiiooietreii per sec., 
an error of o'l in AV corresponds to an error of 1 kilometre per 
SL-c. An error of 5* in the drift I. apex, or an error of 15* in the 
drift 1 1 . apex, corr^fiponrifi to an <>rror of about i ^ kilometre per sec. 

[ tind the betit position for the drift XL apex Q, to be 

R.A. 7*' 30*, DccL +58" 

the ;;reat circles paasing fairly near it, except for region 6. 

The valuea of /iV are in g(»od agrovment with theory, va the 
following table shows :— 



SAffhM. 


Dtn. (rom Of. 


sliM i>I DfaUn«. 


AV. 


A 


32' 


■53 


■y» 


B 


59' 


•86 


45 


C 


3»' 


•5» 


•30 


V) 


9* 


•16 


•15 


P 


60* 


•87 


■45 


G 


n' 


■95 


•45 



Partly owing to the very large niimber of stars in region G, and 
partly owing to itii resulUi iiot agreeing aii well as those of the 
other regions, 1 made a special investigation, auMividing it into 
four divisimitt. Three of the divinions Hhowod tho two drift*, and, 
&9 far as I could tell, wero in good agreement with theory. Bttt 
the other diviaioit (called Oy). viz., N.P.D. 4o'-52\ R.A. i8''-2o'', 
containing 336 atar», was evidently quite exceptional. The diagram 
ftir it is shown in (ig. 7. It will at once be seen that there is no 
indication here that we Itave to deal with a comb'\u&V\o\L ol \>iio 



52 



Mr £ddington, The S^sUmatw 




drifts. There seems to be a third drift in the direction 
which is apparently as important an either of the two fundaa 
drifts. Whether the exjilanation is that we have here a 
lo<:al drift, or whether there is soma local error in the ( 
uiotious, it will at any rate bo admittod that Gy ia an abn 
region, and no good can be dime by retaining it in our InTe«ti| 
of the nature of the two main drifts which prerail tbroagfaoi 
sky. 

I have accordingly anaJyfwj the gnoni cm-shaped reigioo 




pouDdeil of the thrac remaining diTisions. lis centre ia all 
zo*" 30", N.P.D. 36*. 

Drift I. inmii. 

Nuxalrtrofstan . js-S 45a 

AV . . . I'o -45 

80 . . . 330* lOO* 

The direction of drift II. is now in guod agreement wi 

other regions, and sn are the valciea of hV. Ibv directioo of 
I. ia rather discordant. 



J 



5. Thfi Carrinffton Propttr MotioTui. 



I 




After the greater part of the preceding work haii T>e«n 
pieted, another series of proj-er uiotions became availabj 
discussion. These are the reHulL of a coiuparison betweec 
ringk'u'H Catalogue (mean epoch 1855) and the (Jreenwich 
year Catalogue for 1900, not yet piihliRhwl. This weries in 
about I too f^tars down to magnitude 9*5, all included within 
the pole. Of course the Groftnibnd^e Catalogue overlaps this 
90 of the brighter stars are common to the two catalogues. 

Thackeray hns maiie a comparison of the proper inotiq 
these 90 stars derived from the two catalogues. Krom tl^Ji 
found that the mean accidental di^erence between Orooi 




mv. 1906. 



Motions of the Stars. 



53 



and Carrin^ton proper inolion^ in I'l' per cvntur; io eltbur cu- 
ordinate. If tho accideiitul en-or of either catalogue he a^^amed to 
be the same, the nietin a^icidental isrrr»r uf 11 proper motion will he 
o"8" per century m cither co-ordinate. 

TLu ixjHult of the analysis of tli<> CurrinijtOQ jiroper motions woa 

ft8 follows : — 





Drini. 


Drin.lt. 


Numlwr of »tara , 


530 


630 


kV . . . 


1-30 


y* 


»o . . . 


5* 


140 



A coKpariaon with the results fur the corriiaponding region A 
of Groouibndgu shows fairly good agreement. The unly nota- 
wortty difference is the v«lue f^o of /tV for drift I. For region 
A it itt 1*65 : and Although that value is probably rather high, w« 
should expect a vnhieof at leuat i'50. 

One naturally looks for the explanation of a small value of ^V 
in large accidental error (iiee i; 7). At first sight the ubove- 
meiitioned comparison of Oroombridge and CaiTrngton seemed to 
forbid thifl explanation. However, on reflection it waa realised 
that the compan-son only referred to bright 8tar«, viz., IhoM which 
Groombiidgo olwerved, Kow, the Carrington catalojjiie contains 364 
fitare between iiisignitude g'o an<l i)"5, whilst Oroombridgn doea not 
includi-' lunny stars billow magnitude 8*5. The Greenwich places of 
ihette fainter stars are subject to considerable acoidental error, and we 
cau well suppose tbat the proper motions are tiot nearly so good 
OS thode of tbe brighter starf, for ^'llicll the cumparison wm 
made. 

Moreovar, at about magnitude 8*5 magnitude equation begins to 
he uf importance. In any other region magnitude liquation would 
appear as a systematic error, but in a region iiymmetrical abimt 
the pule it ie equivalent to an accidental ertor. 

Aiiotysiug tbv Carringtou t>tare bright^-r than 8*9 magnitude I 
found 





DcUtl. 


Druen 


dumber of stars . 


383 


386 


»« . . . 


5' 


140' 


AV . . . 


t'40 


•35 



The increAse in AV was very decided.* 

Table IX. shows the analysis. The last colnmn 
number of stars between magnitude 9*0-9*5 ; it is inb 
note that the two drifts ate con?ipicuou s, ao that the law 
extend beyond the ninth magnitude. ' ^ s 'ima aro 
nor tbe minima deep — indicating anu ' Mid 

large accidental error. 

• A V ia Mill too mnsU, but we are eat 
excluded fuot *>UrH u bigb«r valut? oTk^ 
ir we rnnave mnotlier lislf n)A;;niti)de, to 






S4 



Mr Eddiiigton, The SydemcUic 



LX 



Table IX.— CASKiNuTON(inftg. 0-8*9}. 



Dlractlontf. 




CalctOfttad 




ObMrvAd. 


nttanaea 
obaarred — 
calcnlatod. 


Hf. 


Drift I. 


1 Drift II. 

1 


Total. 


flbM 


5° 


51 


1 6 


57 


57 







15' 


48 


7 


55 


54 


- I 


II 


25' 


39 


1 7 


46 


48 


+ 2 




35° 


28 


1 S 


36 


44 


+ 8 




45° 


18 


! 9 


27 


33 


+ 6 




55° 


u 


1 10 


21 


28 


+ 7 




65' 


7 


11 


18 


18 







75° 


4 


i '3 


17 


17 







85' 


^ 


*4 


16 


12 


-4 




95° 


2 


15 


17 


13 


-4 




loS" 


I 


; 16 


■7 


17 





, 


"5' 


I 


'7 


18 


18 







125' 


1 


' 18 


19 


21 


+ 2 


I' 


135' 


I 


>9 


20 


19 


- I 




M5° 


I 


'9 


'20 


21 


+ 1 


1 


155° 


1 


18 


19 


19 







'65' 


I 


1 '7 


18 


17 


- 1 


I 


175° 





i 16 


16 


14 


-2 


1 


185" 





' 15 


15 


12 


-3 




195° 





' 14 


14 


12 


-2 




205° 




J '^ 


14 


13 


- I 




215' 




1 II 


12 


12 







225" 


I 


i 10 

1 


II 


9 


-2 




235° 


I 


i ^ 


10 


9 


- I 


, 


245- 


, 


1 8 


9 


8 


- I 




255° 


, 


7 


8 


9 


+ 1 




265' 




7 


8 


8 







275° 


2 


6 


8 


9 


+ 1 




285° 


2 


6 


8 


8 







295° 


4 


6 


10 


II 


+ 1 




305° 


7 


6 


"3 


16 


+ 3 


1 


3'5° 


1 1 


5 


16 


20 


+ 4 




325' 


iS 


5 


23 


23 





, 


335° 


28 


6 


34 


32 


- 2 


I 


345^ 


39 


b 


45 


44 


-1 


f 


355° 


4S 


6 


54 


55 


+ 1 


I. 


Totals . 


3«3 


3S6 


769 


780 




36 



lev. 1906. 



Motions 0/ tJie .'^ar-n. 



55 



6. Cfiaraeieristug of tAt DriftA, 

It will have been noticed that th* velocity of the first drift 
ilative tu the tiuii i» very much ^eat«r than that of the second, 

le valuw heiDg about — - and 7- respectively. For this reaaon 
h h 

18 lirst drift is very much more prominent than the second in tbo 
|iagrain». But the result of the analysis Ja to show that they 

mtain nearly the oanie iLtimber nf xtant, drift IT. containing a 

lightly greater proportion. Another very unexpected result » 

lat iho proixirtion of drift II. to drift I. stars is very nearly 

>natant in th? different repons, as cum bo eeen by inspection of 
Table VIII. The diitCrilMitiiin of the Htara is excee^lirigly irregular, 

nd wu sbouM hardly bave expected the twu drifts to jiOHsess the 

mie irreyularitics. We kni»w, for instance, that starM are much 

lore numprous near the Galactic plane than elsewhere : we niigbt 
ixpect this to be it pecuUanty due to one drift aEone. Now, the 
Galactic plane passes through region B and part of G, and wo see 

lut actuiilty the apocial abundance of stars thore is due to both 

rifts equally. 

We now further inquire whether thin ronatancy of proportion 
Kteuds to all difltanoes. Do the two drifts form a honioi^uneuuB 

tixturet Wc have iteL'u that the pnvportion in the same in all 

irts of the sky (that we have iiivestii;»ted), but nitiy not the 
fcVBrape diatani* of tlin drift II. stars be difTerent from that of the 
Irift I.? For instance, may iint drift II. be a cluster of stars 

>utaiatUK the sun, and niovin<; relatively to drift L, which 

;prasenta the main hiickgruund of nioro distant stars 1 

Meoji DiMaive/i of the S/ftj"*.— We have deduced the variouB 

>nBtants conne<;te(l with tbo motions of the two drifts of stars 
ffsrithout making use of the wagjiUndi-e. of the proper motlonH. We 

ly now use thene in nnler to learn Komcthiug of the distances of 

le stars. 

Ceteris parilm$, the magnitude of a proper motion will be 

ivenely proportional to the distance of the star. Acconlingly, 
wc use arithmetic: means r>f the proper motions, the results 
leduced will refer to harmonic means of the distances. Tliere ia 
special disadvantage in this under certain circumtttances ; but 

is Deoeuary to bear in mind that in nsing the harmonic mean a 
?iit deal of the oflvantage of taking the average of a laf 
luuiht-r disappears. The stars which happen to be near us I1 
rery groat weight in determining the resulting mean; bat 
ire few in number, and are therefore Lttsentially irregularl 

ribnted. The large nnmher nf niure distant stara on whi 
phouUI prefer to depend bave little effect c 

I have adopted the usual pr&ctice of vd 

lotions; the limit I adopted was to n t 

)ar times the moan (excluding themi 

leet the difficulty; the nominal av 
eully dotermiued mainly by about a 



§6 Mr £ddington. The Systematic lie 

this in mind in conBidering the results about to be given. 
is plenty of room for accidental variations in discusBing 
from 20 stars. 

With the notation of § 2, 

mean value of A(r - V cos 0) 

j e-^j^tlx + rl e-'^xdx 

■' -T ^ -T 

= X = •<x, - ,-<o* 

I e-'^xdx-i-Tj e-^dx 

• -T ■ - T 

which after some reduction gives 

" e'^dx 

■T 
J -T 



•' -T 



hr 



-, V TT J .r 1 



Ar) 



The following table gives the valuea of hf correspondiug to 
values of r. From these I drew a graph which gave intern 
values with sufficient accuracy. 



T 


hr 


'. - 10 


■565 


i -o"5 


701 





•«86 


+ 02 


•977 


1 +0-5 


1-134 


! +07 


j I -'52 


+ I'o 


I 449 


+ 1-3 


1 I 669 


+ 1-6 


' 1-908 



Now if, out of n stars moving in a certain direction, n, 
to drift I., and for them t = Tj, and n^ belong to drift II., a 
them T = r2, if f/jf/^ are the mean distances of the stars beli 
to tlie two drift^, and if fj is the mean proper motion in 
the n stars, 

then y: = ''L j + ''^ fs 



Xov. 1906. Motions of tfis Stars. 57 

CuDsidering stars in a different directioD we can get another 
umaltaneous equation, and solve the two for — and — . 

&tampU. — In region B, conuder the proper motions in 
directions 

(a) between o* and 20° 
(j8) between 130' and 160' 

(a) The analysis nhowed that we have here 134 drift I. stars 
and 13 drift II. stars. 

Also for drift I., hY= 1*55 and the direction of drift I. is 10°, 
which is also the mean direction of these proper motions. 

Ti = r55co8o' = r55 
Similarly, 

Tj = '45 cos I 20° = - '22 

From the graph I found, 
corresponding to 

'■1= »*55. hr^=iB-j 
T^= -'22, hr^ = o'&i 

Also the mean proper motion came to be 5''44, rejecting seven 
stars whose proper motions exceeded 4 x 5"'44. 
Substituting these valnes in equation (i), 

5-44'='^'^ xr87x-i- + A3_x.8ix ' . . (2) 

137 K 137 H 

(p) These are all drift II. stars, 

T2 = "45 cos 15' = '43 

hence hT„= vog 

The mean P.M. was found to be $"'0^, rejecting six stars whose 
P.M.'s exceeded 4 x s'o;, 

hence ^,^ = ^-0^ . . (3) 

Solving (2) and (3) we find 



Iu2^ 



^-s- =3' '09 j-T- = 2""82 (unit of time= 1 century) 
The results of a similar examination of the other regions are 



A z"-?? I 3'-6S 

B 3' -09 2' '82 

C 2'-83 3''-47 

3"'34 3"'4S 



58 



Mr Eddington, The Syttemaiic 



UCVJI. 



It will be w-cn that the maxitnuni differencv hiiCWft*>D Ch« 
Dtunbere in the last two culumos U only 25 per cent, of tha whole. 
This perhaps in tbo only coitcluaion which can be conaidered ectab- 
lidhMl hy the investigation. The figures seem to indicate that where 
the drift L atan are neart*r to na Lbnit the avcm^je, there also the ilrifi 
1 1, stars are nearer, just aa we found that where the etan of oue drift 
were densely distrtlmt«Nl, there a\*x} the Rtara of tho other drift were 
denae. However, th«> main conclusion ia that there is no Rppr<>ciaMe 
dtfferoncu in tho mt>an liiHinnciui of drift I. and drift II. iilara 

Mn'jnitude and tipectral Type. — W9 cannot, aa a rule, pick out 
an iodividiinl star and decide (from iti motion) to which drift it 
belong But, for example, in region O we fiodf on reforcuoe to 
Table Vlt., that of atare moTing in direotioos 

9-"390*~36o' 257 belong to drift I. and 48 to drift II. 
for *- 9o'-i7o' 25 ., „ 330 

We msy thus roughly aopanttv out star?) typical of the two 
drifta and v^xamine ibeir cbatnctertstice. 

The following table ahows how ntAN nf diHerfiit ma(rnitudea 
w divided between Uw drifta : — 



1 


VmAot or aiws of UwOlnte 




l-D-4-9 

5 

4 


SO 


4S 3fi 

481 JO 


r*-?"? 


r^a-4 


>■•-••< 


l^ML 




at 

18 


aa 
■6 


II 
■3 


IS 


■^""(dSuil: 




ID 


3S 


to 


47 

3» 


3* 


3S 

SO 


19 


SH 


W.-U. r / Drift 1. . 

"•«""*'l Drift n.. 




'J 


»3 


u 


S3 
44 


SI 
55 


S 


SI 

»5 


3; 


A.B.in<IGf Driri I. 
•oai)<in«l 1 Dnfi IL 


16 


»9 


86 

81 


i7» 
169 


136 

US 


108 
"3 


104 
13J 


1: 


701 
707 


rt,^..-^„, f Drift L 
"^"•^tDriftU. 


1 








4 
6 


ti t i 


16 


4* 

34 


77 
9* 


'.ii 



1 

* 



There ia a slightly greater pro}>orttou of very fainl «tan in drift 
11. in each oue. Tbia may be dnn t<> the fact that accidental err«n- 
tflnda to falsely irtciwuelhe nnnil>erof stars a[>|mrtMitly in drift II. m 
tbia invoati^ation, tecause, for example, ia rv\i^o\i B, • 350* - 30* 
haa been taken to typify drift I., and 0* 190* ~ 270' for drift II. If 
a star's motion is purely iri^tdentsl, tben^ is a miich gnvter chaoc* 
of its falling within the 1 )ttf r than within the former angiilar 
interval 

Most of tbo ver>' bright stars sm>ni to belong to drift I., btlt 
ifaay are few in nuuiWr aliogether. With this fiossible exceptioo, 
we may conclude that tlie drifta do not differ at all as regards th« 
i—jnltiirliii of the stars tb^ oontain. 



1 




Motitms of the Stars. 



59 



w^ 



As regards tt/pe of $p*etrHm, the evidence is incj)iic1a]tive. The 

proportiuii ul ty()t> II. stare seeins distinctly higher in drift II. tliaii 

drift 1. This is true iu every region I have «xBmioeiI. On ihr. 

«r hand, the distiibntioii of speutral types .seems to be deter- 
mined niainly by Aomuthing in no way connected vltb the drift 
uiottous. 

TUf follou-iiig 18 the reaiill of the exauiination of the four 
DUMi snitAble regions : — 



Hm» 



Drift L 



Ko. of Tto. or 










95 
58 
61 
6l 



35 

39 

66 



lUUo 



'37 
•67 

■38 

t oS 



DHnii. 


Ratio 

ColUIDD T. 

Cohumi. 


Tfp»I. 


Type II. 


Katto 
Trptii. 

TJPBI. 


6i 

4t 
l6 

36 

1 


4S 

39 
l6 

TO 


74 
■95 

IVO 

'94 


a-o 

i'4 

2-6 
1-8 



The numbers in the lost column repreaent 

Ratio of Type II. to Type I. for Drift II. 



i 



Ratio of Typo II. to Type I. for Drift I. 

d shuw that in etch case the proportion of type IL tttar* ts higher 
drift II. 

We roust beware of attaching too iimcli KigniJicance to this 
t, and reuitiinber that it applies oniy to a small part of the sky. 



7. Kffn't 0/ Errors in tlte P-ropt-r Motions. 

Accidental J-Jrror. — TUtj method 1 have adopted in open to the 
objection that thti nturs with very »iuu1[ proper motiuus, whose 
directtnn.4 are presumably not so reliably determined, have the 
same weight as those with Urge proper motioDH. We atn, hnvrever, 
take account uf small accidetital error in the followinj; mauTier. 

If the unniber of stais having on actual velocity component u 
be N«"*^' and the prolnability of an aocidcntat error x in the 
observed component proper motion is 

{x htiuii a linear reloeity, nc con^e our attention for the moment 
to Btitra at n definite distance). 

Then ttie number of itars baring an tiheerved velocity u is 




Nr'c-**--"'-4#-'^(/flr 




6o 



Hfr Eddxntfton, The SysteauUic 



Lxvn. I. 



which reducfvi to 






ThoB tbe ofTect of accidental ern>r u simply to chuigt 
true drill coiutuit /t inlo tui apiKtreut drift coDatatit /i, given bj 

Tite moan accitienUU «rrur ul a nroorabridK^ proper tnotfon 
ftppean to be about o'8' per century ia eitlier co-ordinate (w« p. 53). 

To eonfert thia into linear velocity we must om i\w valaea of -^ 

found in § 6 : tha meui value oi ~ '\»% little onr 3' per century, 

banco tbe mean accidental error id the component lioeai- veloei^ 
of aatar ia 

<'X!--*boiitI- 

3 A 4ft 

a 

But if the probability uf an accidental error x be —7= 

the mean error u , 



wbenee 



I "09 -T- roughly 

A 



Tfana ibe effect of occidpntal error is that if the true valu**' 
A is naad, tlie (|Uaiitities hV ^'iveu tn the preceding MCtiuni sbouUl 
lie incrMued by about 10 per cent. 

Sinoa ff depends on tbe distance of tbe »t*rB> this correction is 
only approxiriiste, and wiiuld not hold if the accidental error were 
large. 

Sffttttnaiic Error. — It is ptMitible that in any region all tha 
pro|wr motions may be liable to ■ ijratematic error. For various 
reaaoiM it can b« mntldently averted tliat ib no eaae doea th« 
syatamatio emr mnch «xce«Kl 1' per centary. For instance, let 
mt3^ proper motion be repreanted by a [toint whose CartiWaa 
eiHirduMtca are it* oomponenta; if then Is no ayatematio •mr 
thaae poiota vdU b« deoaast near the origin, but if there ia ooo- 
aidocmble systematic error thi« will tioi bo so. I have ezamiitad tba 
man Important re^ioas ia ihts way and found no indication of 
lai^ syslelaaUc emir. 

Table X. shows llie number of proper motiona which are 
i;r«at«r than 5' per c*nLury in earb region in tbe various directions. 
This tabls can hardly l>e appreciably affected by any admissibla 
valuv of the syilamatio errur. Nevcrthelaas. the presence of two 



i 



1906. Motions of th* Stars, 61 ' 

1 


Tablb X.— Pbopbr MonoxB izcekdino 5'. 




. 1 BMIOII 1 








CkrriUF- 




, 


. 1 B 


(1 


D 


K 


V 




7 


lol). 

33 




5" 


*9 38 


a 


4 


»S' 


33 


31 




I 


J 




S 


30 




*r 


16 


32 




1 


2 




7 


*i 


1 


35* 


10 


15 




» 


z 




4 


iS 




45' 


' 


10 




3 


3 




3 


>4 


1 


55' 








5 


3 




3 


10 


' 


65' 








6 


3 




5 


8 




75' 








7 


a 




7 


7 




85' 








8 


3 




10 


5 




95* 








10 


3 




II 


4 




'OS' 








IS 


4 




10 6 




'■5" 








iS 


4 




10 5 




.25' 








18 


7 




II 6 




<i5' 








>5 


b 




13 7 




-45* 








13 


II 




It 


9 




ISS* 








9 


12 




7 


8 




.65* 








7 


16 




4 






'75' 








S 


21 




3 






>S5* 








5 


22 




4 






•W' 








3 


19 




4 






*>S' 






1 


a 


12 


10 


3 






215- 









1 


8 


13 


3 






"5' 











6 


15 


2 






»35' 








I 4 


12 


2 






245' 






1 


2 3 


9 


4 






»55' 








1 


2 


6 


7 






26s' 








1 


3 




10 






275' ' 










t 




10 






28s* 2 










O' 




IS 




' 


"95* 3 







1 


a 




>i 


4 1 


305' 1 4 















Ijl 


^^A 




315° 7 










I 




4i^H 


► 


3^5' 9 







1 


t 


1 


^1 




335" 


M 


lo 


o 


1 


X 


I 


1 


i ***' 


» 


22 


« 


2 


4 




1 


L 355" ! a6 


3i 


[^ 


1^^ ' 


^^^ 


UloB drift II. 170* 


qS 


■ 


■ 


L 




^^B 


I. 


^ 


■■ 


m 




!■ 


J 


r 


■ 




J 


^^m 



62 Mr JCddiiigton, SyBtematie Motums of the Start. LXVli. t, 

drifts it exhibited roty clearly ; in fact^ more so than when all tba< 
prD|wr niotioiis nre included. We may thervfnn' fi-ol mm Umt thtt 
phenomena which we li&ve atlrilmted to two drifU arr r«al, and not 
in any way the effect oi systnnmtir cr^or. 

A calculiiti-u uf the |io«itioQit of the two apicM from thiM lux*1 
proper niotioiKt ^aves fnr 

Q, K.A. I8^ Decl.+ io* 

Q, R.A. 7\ DeflL + 58* 

iD quita good uuuugh OficrLHtiuezit with thuiM* previotuty found. 

A very im|H>rtant {KKtsiliU* Kystcmatic err»r — that due to 
iDcomct ooDSUint of preceMion^niuot now be luiofly cormidert 



& The Oondant of FneeMtian. 

The determination of tlin proper motion of a fiUr depend* 
cotnpariflou uf olMervatiuuH uf itx jKiMition tvfemHl to certain axi 
at different e)>ocli». In thiti com^>ariB'>ii two uiiknowuii nrr con- 
cerued, via. the motion of l)ie axe« of n^r»roiice and the motion of 
Uie rtor. The lamu holds truo when we ronnider a large nomber 
of Stan : there arc two unknowiki — the nioliuu of the rzm and th« 
syHtumaltc oiotioni nf the eiara. For this n«soii, iu formtr inveati- 
gatiouH, determinntioiis of thu solar motiou and of the constant uf 
prfloeerioD were nflcasRahly iiiodo tost*thar. The qoeetion ariaea : 
Can we attnclc the fundamental lusumptionH ou which the determina- 
tion oi the «olar motion was made without ettacking the value of 
the preceaaioa-oonstant found at the Mme Umf ? 

ThU ia a serious queetion from the point of view of the pretetit 
paper, Itecaune the cunstnictive ami 4{Uiintitative work in it depend* 
on the o»nvctooiw of the Struve-pftorx prvcemiona. Aa Dyaon and 
Thackf^ray poiutod out, tba ar«a covered by the Qrounitrn<]gv 
catalogue is not rary sensitive to a ohaiige in the Talue of tb« 
prwMancia. 

If Newoomh's prvceMotie were adopted, the corrvction to th« 
proper molione would, in the extreme cases (regions C and D), only 
amount U' o'S' pnr century. Diik would m^e very little diffur- 
enoe in my tablea. Hut may not a tnuoh more widely diffemit 
\*a]u« of the prrceswon be admiiwiblet 

There is an a fXMfmor'i justification for usine the usual valua 
of thn preoaaiion-eODetant. W« hava arrirad at the conclusion that 
tbo two drifts form a practically faoroogUMOut mixture. If, and 
only if, this ii the case, Airy'^ meth'jd will pre the praceMton. Aa 
far as avLTUftm an< iimc-emod, a liom'>g<'ne>ms mixture of two 
drifts is equivniunt lo a piiiiL^ln drift. T)iu« the eo-called aulw 
motion ia an un{)orirint niatht^niulicol vector, but its pfaydoal 
meaning mint bo modified. Wr must not be rarpriBCil st tba 
diaoonlancas which tMx-ur in iho veriou* attempta to eetimafa* it; 
it only existft at all WrjitiM n( this mni^hly nniform armngaoxint of 
tba drifts, and the precision irith which it can be defined depauda 
on this uniformity. 



4 



4 




^ 



Nov. 1906. Mr JHummer, 0% Uie Jiff«ct& 0/ Jiadiaiwn, etc. 63 

We ooncludu that tho adopted value of the precession is not 
widely wrong ; at the name tinif, if our theory* is correct, we miiBt 
nut tnut too f&T the pi-esent methuclA of cakiilfttin^ it. Tbey are 
only approximately (and one might almost say accidentally) correct. 



9. Suntniari/ and SeaJtu. 

The Greeriwich-Groombridge and Oreenwicli-Carrinirton proper 
mottciius BtruuKly support Kapteyn's hypoihRsis of two star-drifts. 

The ntMitional rexnlts arrived at in tikis paper (which, of coarse^ 
depend ou the truth of this bypt'thesis) ar« : — 

1. The Dumben of the stars belonging to tho two drifU are 
u early ecjuaL 

2. One drift is moving rplatively to the fltin, with a spe«d 
bvtwe«n three and four timefl that of the other. 

3. The proportion of ntani belonging to eadi drift is about the 
le in vrery part of the »ky and at every distance hero dealt with. 

4. The magnitudes of the stam belonginjj; to thf< two drifts are 
atwut the same. 

5. The spectral types of the Ktara iteem to diflfer to wme extent 
in the two drifts, lint the evidence is not coiichiaivc. 

6. The results apply t4i all htars down to magnitude 9'5. 

Ropal Otmirmtory, OrecAurich : 
1906 Atigtu*. 



I 



On t/te E^fci« iff Radiation on the Motion of Comets 
{Second Note). By H. C. Plummer, M.A. 

]. Professor Poynting has recently pointed out to me the 
ttence of an additional term in the forces which are due to the 
n of ftolar mdiation on a ftiiiall black body. The tertii has no 
Wt when the motion of the ^ntrlicle is rirnular, but it becomes 
necessary to amend the theory which was given in ^ 5-8 of my 
former paper {Monthly Soticw, vol. Ix\'. p. 233). This is due to 

tbe fact that when the body is moving with u radial %'elocity-T# 

the light preftsore is altered in the ratio i : 1 - -p • -r. where U is 

the velocity of light. Tho etTect of the radial component of the 
niotion wa.- before omitt-ml. 

}. The radial accelt^ratious of the particle are 

(i.) that due to gravilatiou, 




64 Mr H. C. Flwmmer, On ilie Effects of urfl 

(ii.) that caused by a "static " preuara due to 

(iii.) that caused b; a '* kinetic" preaaore doe to nd& 
(tlLia u the term iiuw iiit.rocluoe>l), 

There is also a taugenttal ret«rdatio(i Tv/r^. which 019 
resolved iuto 

(iv.) a radial component 

^ r^'di 
(v.) a tranavoreal component 

T J6 



V.= - 



dt 



Now if S is the aoliar coimtant m the Kartb'a distuica b 
the Sun, anJ a it. the radiui 



liuB of the sphorical particle of deoiilTH 



Hetice the cuniplute radial component is 

3, One equation of motion remaimt as before 

or on integration 

r'-.-=h=-(T-e0) 
at c 

where e in a Binall constant ol the aame order as T. The 
equation of motion is 

which becomes on eliminatmg t and putting u= i/r 

Hy (3) and {4) this is reduced to 

t/^ I - rtf ./* (I - r*)"!'* 



Nov. 1906. JiaUi€Uwn on Uu Motion of Comeis. 



65 



which differs from tho coiredponding eqaelion of the former paper 
by the addiliuii of t>it) third tertii uii the Uft. 

4. Negiecliog second-order tvrma wc rvplnce (5) by 

u integml of which, to tho same order of approximation, is 

i»-{/i-/)c»T-«{i + actf + eco8(fl-y)-2<;«#co8(P-7)) (6) 
i>t the osculating orlNt at tb» [juiiit B be 

Since r, — - aad -~ are the same for the two curvea, u, — and A 
dt (U d$ 

are also the sams. Therefore bj (-1) 

h» Tf(i-ctf)» 

r 



^ 



whorv tf is to be coaiidered couaUnt at the {>oiiit. Hance we have 



(M-/)o» 



<;» 



= I + jcfi + e coe (tf - y ) - 5«5 CO! (tf - y) 

= (i + 2ctf){i+*!'cM(tf-y')} 



aod also -~ the same for both exjireflsiotiA, {irovided that in the 

aeooDd we regAni cff as constant. Hence, still neijlecting terms 
beyond the Hrat order, 

e' cos (tf - y') - e cos (tf - y) = - ^ceS cm($~y) 
e*8in(tf-y')-esiii{tf-y)= -l<«^8in (0 - y) -t- ^eecos{6 - y) ~ ac 

From these csa bo derived 

Sfl=. -h:e$ + ^^»m2{$-y)~ 2CBin(fl-y) . (8J 
e . Sy = - |ce ctw* (tf - y) + 2/: tl>8 (tf - y) . {9) 

where the incrementii refer to the osciulnting ellip»o or corii|jared 
with tlie etli[i»e obtaiued by BUitpressiii); tho auceiita on e and y. 

5. The secular chaiig(% in tho oletucMits cuu xiow be de'lu''ed 
from (7), (S), and (9) b; considering the eSbct of a coinploto 
reTolutran. The roanlt of thus removing the periodic variations 
11 oleorljr 

AV/=-4irc .... (10) 

^/<« -fwe . . ■ (11) 

Ay^o (is) 

Thus the result of the additional tprm in tho action of eolar 
radiaiion is by < 1 1 ) lo iucTease the secular change in the eccentricity 
in the mlio of 7 : 4. 
Further, 

ire . . (ij) 




T-^l-ei 



i-e« 



66 Mr H. C. Piammer, On. thf EffmU of Radiation. Lxvii. i 



And 



Tht 






J« 



. (u) 



effect of the a«ir t«rui ia thus to iocreaae the change in Uie 
metn motion in tha ratio 

•0 lliat, with thv MIQ19 notation an<l conatantA as liaforv, cquatioil 
(1) of the prvvinus p»{H'r U'corne* 






6. For Kneke'i CkiBiot, >! ~ 0*85, vti now obtain 

/M -0*0093 fnn./cni.- ; ti-'lfi~o'oo& 

Thtm Bgitm do not dtffor very matvriaJly fmm tho«fl praviouoly 
found. They ar« of the same ordvr, and e(]U'illy fnil Ut iiubalnntinto 
the auiRtestioti that hh aoceleniion in the moan tnolion uf Kiirk*:>'« 
Cunift can bo exjilainetl in thin i^iarticular way. Thi« concluiiion, 
thongb diaappoiutiuKt i* only what tniffht huTu been antioipatecL 
Of the forces <?nuQieral<Hl in § 2, tho cuiuponeutB (iii.), (iv.), and (v.), 
as coDpond with (ii.), thu direct rniliation |ir««aure, are of the 
aame order an cometary T«)o<Titiefl compared with the Tolodtj of 
light, Tbair effect ii iberefnrv naturally fHr smaller, and can only 
bvcotne adeijoate to explain a coitapicuuuii inequality when the 
f;rmvit4ition t^nstunt itself is eSi-cUvely dttniiiishi'<l by t)tc back 
pressure duu to nuliation. The forces wliich depend on tlis 
Telocity of the comet arc diivii|>ntive, as I'mfessor Poynting notioM^ 
and thereroro curaulativu in vlTcct. But tfaou^fh their influsnca 
may thus boeonto of th« gnsteat im|>ortanc« by the Up!>e uf timv, 
it ia the eonaarvativQ component of which eridaucc must fint be 
expected from direct observation. 

7. Stnm my earlier jHiiwr the queetion of evidence im this point 
has adraucod, and wu now know that us lung a^'o as iS9t tha late 
Dr August Hveilstrnp had Wn led by hix Inbuure on tbo ootioa 
of Comet 18&6 I. to thi> conciuston thnt the conntant of tolar 
attraction was in this rase effectively diminished. The result is 
the more remarkable that the author RoemH to have been nn- 
inflaaaoed by any hypothesis m to the action of radiation. 
place of the Oaoasiaa oonstant k, he found it ucce— iry U> 
(A-N., 4o6», p. 98) 

K-»i:(l - 0-0000415) 



I 

(15) J 



4 



which {(ives 
Hence 



///t- I - K'/A'-o'ooooSj 



•P 



3 « 5^ 

4 ' t? * ^ ■ 
w 0*89 gin./eiH.* 



10" 
83 




Mi- Plammer, JCeplcr's Equation. 



67 



if we atinpt S — 175 « 10". TliU «how» that if p is about. 6, 

or Bumetbing Hke the iiiean tleiwity i>f Uie Earth, the diameter 

of the particles cutiipoaiug the comet ie of the order of 3 mm. 

This result coiiliniiB ilia liji>otheKiH as to the pbyRicul coiislitu- 

tioD nf comete on which this itives ligation rcats, and soppUes thn 

£ntt nuiiiericol etttimatt* of the nize of the meteoric bodies vhich 

constitute a cometarjr swarm. 

. 8. Dr Sved-itrup'd discovory amply justifioB the atatemeat 

before made, that "it is unwarrantiihle to Q*eutiw that the mPAn 

' motioD and the nicAn dlRlancei are rtilaled and nut indepemleiit 

I elements." Thi» musl be borne in utnd in all future dUcussioDS 

I of the delinilivo urbitH uf comets ; otherwise a vuiuable mutinn nf 

gaining an insight into the eoustitntion of these bodies will be 

»neglActed. It now appears exceedingly probabto that in this 
direction Hex the clue to the expUnattou nf the anomalous motion 
of EuL-ke'ti Comet, a& HUg^st^'-d in >) 3 of my sarlier paper. 
r 
Kulut 



Dttivenitjf OtmerwUcirif, Orforti : 
tgo6 Atirjuft 18. 



Note OH a Meeftanirai Soiutton of Kepier'n EtfWttUm. 
By H. C. Pluminer, M.A. 



This note refers to the niethod of obtaining an a[)pruximate 
solution of Keplur'n equation which Wiui propoiied by l>r Ramliaut 
(Mon/JUt/ iVo/icec, vol. I. |'. 301), und was subsequently doecriliod 
independently by myself (MfntMij Notu-ea, vol. Ivi. p. 317), and 
again lat«r by Herr B. Gonggrijp (.-l^f^. Nadi., 3720). The principle 
uf the method, which is iMiued ou tbo utie uf a trochoid, in to be 
found in Newt<.tu'8 Priticipia, bcwk L prop. 31. 

Quite mrently Dr Uumbaut hiis proponed a new roethod which 
combines gruit mathematical cK^ance with considarabte practical 
adrantages {MontfUy Noti6ef, vol. Ixvi. p. 519). Uis paper 
suggests that it may not be out of pUce if I deiUTibe some 
modificatious in the application of the tmchi^id principle which 
Docarred to me, by a curious tuiiueidGiice, about the mme time. 

In the accompanying tigure, ARC is a flat circular disc of 
Boitable ndius, mounted on a board no dh to be capable of turriing 
about itn centre O. Fixed to the board and Hush with the surface 
of the disc are wooden pieces Y V, N N, which nerve as guides to a 
acale Ss, which, with bevelled edge-s caTi nlide between them. 
The point G, marked with a pointer, is tha foot of the perpendicular 
from O ou tho tower edi:e of the scale. Attached nrtar B, and 
pauing round tlit.* cd^e of the iHhc, is a tbiii flnxible metallic ta[ie F, 
the other end of which in attacbeil to the end of the scale S B 
This tape is kept taut by another tape BCP passing round the disc 
in the uppoAiU direction and fastened to a weak spring or, much 
better, to a tiauging weight. 



6S 



Mr //. C Plummrr, Xote on a Merhanieal LXTll. i. 



The rotation of thi* disc thus depends nn and t»n be moMsnmd 
by the motion of the scale R 8, ■ pnrt of wbicfa. in length e«]tul to 
half the circumferenon of iho disc, ii divided into iSo' in eneli • 
way thiit the origin coincidee with th« point E when the ndius O A^ 
u perperidirutur to the eoile. Then olcarly the |Kiintf>r R at any 
tbna marks ttii< luiirle (< tSo*) through which the diao has Iwen 
turned fmm its initial |Kisltion. 

The initial radius O A ifl diriditd in fractions of its«tf (nashowit, 
in t<>nths), so that a Ien;;t)i ( )•■ ran bs taken oorrfsponding to th^ 
occontrii'ity, the whole rndius l>einfi unity. The Inwor ed(^ of th« 
guide N K is parallel lo the scale 8 8, ao that the edge of a T-squar« 



I 




T T can be kept periwndicular to the scale. The instniment uin now 
bp usad to find no approKJmale sulatiuu of Kepler's Mjnaiion. aooord- 
ing tn till' followtii^ rule:— 

/Va« th* t'Jtje u( thr T-m/uart at tkn it^utintj M on thu aaUe 8 8. 
Move the in-ale and T-n^uare togtdhrr tiU the fMimt e on O A tehiA 
markM the frrtm/ririti/ e /■iU$ tm tht mttjt of th* T-^quare, ThfH 
Ttwl flt^ fMMiiion of Ihr fniin/rr K on f A« toaU. Th^ rtaiiing m th$ 
wooenirir anomalfj E corri-jijHM'Unjf to the mean anoni'dy M. 

For daarly 

E-M«erinE . • <') 

If M lie* Acfwara i8o* and 360*, mss Mfi inidramtnt aixorSinff 
In thr alior- ruU fofind 360' - KfftfH j6o' - M. 

Tha*ij{nm iidrnwii furr- o*65,»bowiiigM =» 3s''<3*"^ E"70'*O. 
The njlliiitf diMi of thn derlo^ formerly described, with it* tnniblfr- 
■ona manipulatiOD »nd liability to error, U now fliminated- The 
prmtait uutrnmanl is Dearly as simple to use as a shdo-nile, and 



M 



* 
* 



Nov. 1906. 



Soiuium. of KepUr's Equation, 



69 



* 



I 



it has the ^eat advantBge of being ilirect-reaciing. Tn-o Btraight, 
imiforuily divided scile^ OA atid S8 utonr ara necessary; and 
the ucciuvcv uf reading can be increased by placing u vernier iusUsutl 
of a ttimplo poiiiUT at \i, and atlHcliiiii; unutliLT vernier to the 
T-wjoare at M. The surface of the scale S S should be very 
sliffhtly shore the level ui Y V, N N and the \\Uc. Tbe T-square 
can then b« kept nt a h^cud reading wilh one hand vrhile Ihe i^cale 
is being niovwl by t^ic otlier. It woidd bo still hotter if the head 
of the T-squtre moved along a groove in tlie scale itself. In encb 
dataiU of canatritctioa there u naturally much room fur variety, but 
it is possible to make iiii iustrumeut ou these (^^eucral Hues whiuh is 
both aimpio and efficient. 

There are, however, three additional «c&Ees shown in the figure 
which may Ik; briefly cxi'lained. The first is on the edge of the 
T-aquare, which is graduated in fractions of the radius uf the disc. 
The ori}>iu of thiit scuU' in on a level with the luuroiit [joiui of the 
cili»c It id thuti )>ositible tn road direi:tly at the [triint P- the height 
of this point above the lowest jmint of the disc, and this reading 
iilearly corresponds to the (jiitinttty 

l-ecosK=-=.-^ ... (2) 

This is the ratio of the radius vector tu thu mean diatauce, but 
its more important signilicance arises from the fact that it is the 
ratio of correAponding increnienls of the mean and eccentric 
anomalies. Tba* when an approximate K (a^ found by mechanical 
means or othurwiHe) is known, and in fuund to lead to an error (Af 
in M, the apprDxiinate ern<r in the ux^tutnod K iii found by dividing 
dM by the reading on thn edge of thu T-itiptare at the jioint where 
it is crossed by the radius O.A of the diiic. In the M«e repreaented 
iu the figure thin reading 8hv>ti]d be 0778. 

Up to tbi» point wu have cunsidored only practioid modlBcatlous 
iu applying tho principles of a device fonn^Tly described. The 
graduation of one Bsinicircle and the unequally divide! scale on 
the radius OB. as nhown in the figure, are dne to an addition 
which, whatever \\a v&Uk'. iippr'am to Im new. Thu ubjei:t of this 
is to obttiiu by a direct reading an approxttimte value of the true 
anomaly. The graduations in the radius OB (nuiubcre^l in the 
figure for loe) are made in sucli a way that correspouding to any 
aocentricity e a point/ can be read otl' such that 

Q/7OB = tan ^ 1^ where sin ^ = e 

A thread C D is attached to the point C, the highest point of the 
disc. The dine bein^ in the po.'^ition niready fonnd, the thread is 
stratched over the point / and cnuwes the edge uf the disc at o. 
Tlien the angle AOtr or r is such that 

feauJi;=yj-±|taniE ... (3) 

■u tbftt f is the true anomaly corresponding to tho meau &&omv).Vj T\- 



Mr ffinks, .SWar Partdlax Fapert, JVo. 5. LXTll. 




Tfafl gMim»tricnl principle on which this Tory simpin clerics ii 
ii«ed Dot be proved lieiv.* Au accurate viilue of ihe tniv mnc 
can only 1h) found \i\ cftlcuktioti from an uccuntu* vnlu»> of 
Hot there may be ca^^eo in which only ■ futgU valuu u r«qutrMl, 
nnd in any oue a Taluu of Uiia kind, whmi no easily obtaioed, may 
)« Dsefiil in preTcnting auy serious Ai\} in the calculation from 
U-ing overlooked. In the caM* reprcatfOted in the figurt) tha vmtaa 
of p uliould bo 1 13*'3- 

Tbo oomplete instrument thus providca th<- nii'«na i>f fmtling, 
for any valuv of the uccentricily batwaon o'l and 0*9, approxi- 
mat« viduoa of the eccentrie and true anoinalioti nnd of th^ rtt'liuA 
rector, when the nixun anonmly or tiiu« is };iveu. It thu* anlvtw 
in ui approxin»t«> manner thr whole problem of elliptic motion aa 
nxprcsiwd by the rvlationa (i), (3), nnd (3), and ihi! ea«a with 
wliich ihiA (-an be done auKfimta tliut thf inatniniont may hnvr 
aonie ali^jht eduattioniU m well a» practical value, 

1906 SrjilfmUr I& 



Sotar f^trttitax I'ttpm-*. No. 5. 

£samtnation 0/ the Itiotoffraj^tic. Ptaeag uf A/ar» /rtiitiiMked mi 
the Pitri* Ktm Cirtulart. Hy Arthur It llinka, M.A. 

1. In a procediuK pj'por, Salttr /'arailax Paiterr, .Vo. 4 (ifonthlf 
A*06mi, 1906 .lunc, Uvi. p. 481), It wan ibown tlial tlic pluit'v 
(fnphic right aat-ensionA nf rr/H^ry ttam, pitbltshed tn Parix olrculam 
10 and II, had littlo if any magnitiidu epilation biwciaI to vmch 
obaervatory (witli one exctiptiun) ; and thit ccnrliijuoti wiu» drawn 
that it u uidikoly that tliuy liave nn abavlutc nidt'uiludn i>(|tiation 
commoD to all. Thin applif^a unly to atara down to a nmgnitnde 
little fainter than 9th. In tbo pn-Mnt jMper 1 propoae to tutend 
the aearch fur phutuf^phic inagnitaUr equation to tbi 
docUlutiona of the rrprn tiKnn, uiid to ih« fainter vtars in botJi 
oo>ordinftt«B ; and to look for Hyvt^^matii' enxm other than tfaoee 
depending on magnitudr, m* fur oa they can br detocted by inter 
eompari»un of publttihnil rrMilt«. 

2. Tlic Rtan uieaMun'd ii|Hin Kroa ftlatea in accordanoe with 
M LoewyV pni^nnuiinc tire divided into thrav claseea: — 

i. The ^tmlen lU rt/*^ eitendiii^ riyht u|i to the edges of platM 
f ' aquiir4>, anil g«ndrally in the otitt*r regioaa rather than near llw 
cetitre. 

ii. The HoHe$ tie lUampamurfit^ which have Iteen tuied aa eoa- 
panaoii atom in vinual micromeiric obaervatioit*. They tif tnoatljr 
til a narrow belt iilung the track of the pUoot, and extend right up^g 
to two ad^oa uf the plate. fl 

* Th« i<riu<-^>I« ia ilie mbw u tbftt «ii<|>li)yMl In " A Mnthod (if Mnliaat- 
nlly Cara|>mwlin£ th<' KoUUonof tb« Kldld of » SI(l»ro*UI "(Jtf..V.. vol. IxL 
p. 40a>. S99ijhi» iijoof wbleh mn Im> 4iUpt*l wilhaut difflcolty to tha 
^raiaaloaM, a(>d||8sn<i9lbr ■nvxamintlioDdi thegvoiuvtry nfihuprla'-lpU, 



ov. 1906. Tlie Pkoiographic Places of Stars. fi 



,0 


V — 


t*\ 


" 


* 








1 + 


1 + 


+ 


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1""', II1+ + -H++ ++III + ': I 
— -..i^i-ntn^^— -^ ■ — ■ — ^ ^ ■~1' -ii- 



£"1 + 1+ + + + + + ++I '+j;^' : "•" 



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73 



Mr ffiiih, .Solar ParailamFafm, Ab. 5. UCTH. I. 




Ui. Tbe MaiUg du carri de ao', including all cun on the pUt« 
within a Mjiiare of tweuly uiinutM of art, baviii;^ the planet at the 
centre — the planet being alwajrs near the ccutrv uf the plate. 

Unforluiiatvljr fur the stud; of njnteniBttt! nrorM, thi! pUoea of 
the Ktara in these thr«n rAtei;onc8 have been pnblialieil in three 
different ways in tbu Fans Cir.aliint' 

Fur the eiuitw fit; re/'cre, Tublean I. f^ivts the mean plfeoe 000- 
cludcnl frunt the wliole uiiiuWr vf plat«a. 

For th'- rtoiit^ (ie itmtparauon, Tabb-au III. givw, in mme 
caws, L'oUectioiiB uf the mvporate iuiliviilual ivMultM, but without 
indicatiou of the ptutoe from which thny ore derived ; in otbtr 
caiiieit, niemns unly. 

For tli» I'-tuiie* tfu rarrr the TabJcMU II. gives the complete 
individuoJ n*j>nlt>, plate by plata. 

It is therefon* ini|w)esible to seiMrate completely the proceeds of 
one plate from the rest, and thi« is a grave obstacle to the proper 
iDvesti^ation of the twulta. Fur the prt-seut we are reitrioted t<i the 
study of mean pliu-es (exocpl for a *>niall cuntral region). We shall 
therefore, in what follows, draw nodistinctiun between cla8»«s II. and 
ni., snii HhuU refer to nil the fuiiiter stan) iis '* coiupari«on star*." 

3. Mittjnitiuie EiiuatHm in Pfiotot/ra/'hic DflimUion*. Report 
Star*. — Thi* i-itrii{Mri»iiii of the phutiigrspbic ili!rliii«ti'ma uf ffpert 
stars, grouped according to magnitodp, is pmwntod in tbi; same form 
as WHS the compariwiii of pholo^nipbi^T ICA/a in my IsH |Niper (toe^ 
eit.t p. 483), but with tim addition of a coluuin for Pari* miona 
mean of newn (Algiets being cxclud'*d). 

For list I, HtiitB, Algiora ban a conHiUemble magnittide equation 
in defilination, as it had in ICA. Ban Fernando shows uo verj' 
evident etgn of it ; but Tou1oubi< has a wril-inarhed magnitude 
equation, which is uni'xpectol and very tnti>rv»ting. Bordeatu, 
Catania, GitHvnwich. HeUingfora. Nortbfiotd, and Paris show no 
aerioits divergence onu from another, and we ooochide Ihnt they are 
■oosibly free from mognitudo equntiun. 

The ciiQii'srison with list II. t-xtrnds nt pr«*i*nt only to R.A. 
i^ 1 7"' {corn»iHinding to 1901 Jftrtiiar^- 25). Up to that point 
tliere is little rviilonce of iiiagnttndu C4(U»tioii, wen fi>r Algiert. 

4. MagmihuU iSquation in Vi*ual O^Jinationi'. TucImj'» 
Sjft^m. — This comparison follows very cloeely on tin* lines of tb« 
proceding. 

Compariaon with the niAan of six obe^rvatories (exclndtnfi 
Algiers, Toukituie, and San Fernando), and with thu six indindu- 
ally, shows Ititle or no evidence of any mognilude equation in 
Torker's declinations, unlca* possibly for the brigbteet star*, for 
which material in insuftlciont, 

And the rarioits syitLnms adopti^il by ditferrnt nhservatoriea ahow 
DO certain trace of relative magnitude equation when compand 
irith Toeker. 

Wa may omtclaJe that the meridian circle deolinattona in 
gmnl an pnotioaUy fre* from perminatiiy dei>«ndittg on magnitude 
— an inUnatiiiff and somewhat unexpaotad otmelnrioii. 



I 



I 



L 1906. Tht Pfiotogrwphic Piaee$ 


0/* 5i«r«. 


1 


« ^^n^Oww-• — « 




„ 


M — r^ so f^ 




1 2'+ + + + + + ' + 




P 
1 


«1 ■. — e« 
t 1 1 1 t 1 


, 






^I'm^ 




• 


1 a tn<ia>i-e«:fMr>. 

1 S «pi«^r»»r^Ogirt 




%-% 5i.?S8 •8^"2 




^^^^-""^ 




•h^ 
















1 mOvr**— *^l^^O 


_ 


30 


O; -r M *« ^ 


■V 


;!*^ " 


p 


~ 


r* 


■g ' 1 + I 1 + + T + 


+ 


t 


1 1 1 1 1 1 


; 1 




riB. 


gm^ 




^^, 




t« 


f> 


m r<. — 00 r« <0 


^ 


^ 










,_, •>.* 


^ 


iO(*V«NMOtt^ 


? 


P 


•a « 00 r^ - 


? 


6 " 1 + 1 • + + + + 


+ 


1 


+ 11(11 


. 1 


1 gg -^v^Ar^Jirvvt — 


tn 


t/l 


^ 00 r* Oi »r rj 


•^ 


R: 


"^ 




W 












Nt^V}r(Nr«tit 


3 




■*) m ■»■ «0 ^a !»• 


f*» 


' ^ ~+ + + i t + 1 1 


» 


t 


1 1 t 1 1 t 

_^ ao r> ot * n 


. 1 

5 1 


« 








M 




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w ^^H 


^ ~+ + + 1 1+1 1 


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1 


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^ 1 


+ 


+ 


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1 




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1^ 


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^ 1 


t^ 






^^ ^^ VHid* -*^ X»^ 








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+ 


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1 




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m 


r^ M « <0 0> (^ 


s M 


i*V 












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t«tHi^t>iN — on 

ri *+-*- + + + + + 


3 


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^ 1 


+ 


+ 


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1 1 




,r^ 


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1 


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'O 1 




— w ^ 


2- J 


1 t<.ir>OW'oa9«r^ 


»>!, 





to ^a in in •-• 


^^^1 


>P ~ ~ - 


P 




N •• -■ - - -«■ 




^ " 1 + + + + + + 
■^ *-* ~ n ^ irt rn •*-* 


f 


+ 


1 -« 1 1 1 t 


1 


^^ 


^bv 


^^ ^~« ^^ ^^ «»^ ^^t 


^^ 1 


is. 


^ 


r« <o N vt «o fo 


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00 






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'-' 






^^H 




5 


? 


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^1 


i*^-*- :-^* + 4+ + 


-t- 


( 


lilt t 


^^H 




^■^ 


J- l_ 


^^ *^^ ff^ ^^ r^t ^^ ' 


^^ ^^^^^H 


Hn w ^2^**(r-2 


Ov 


M 


•^ V to *^ ^|B| 


^^^k^^K ^^^^^H 










p ,. - 


" 




"""MB 


^^B* ^^H 


f« Mr^JJi-OO^a^ 


.8 


jA 


« ;.« n^H 


^K ^H 


1^ ss8^5;s"52 


^ 


' 


^1 


^b- ^B 


•A 


m 


- - qu 


^^^5 ^^^1 




n 




"4 


^p ^H 


r* p- .-v >^ ,"* ^ r* 


~- 


., 


j^ nr p 


^ ^1 


■a %o k. r. M aa 






^ r^ f>- 


^^1 


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■■-'■ 


^^M 


<C Kk P« » ao >~ 


H 


■ 


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— M 



74 



Mr Hhihs, Solar Parallax Papers, A'o. 5. UCVU. I, 



Bat the coropamon of Tucker with the photographic resalta o( 
Algiers and Toii]ou»e exhibits the magnitnde equation in the latter 
previously discovereil. 

The rvaulta of thu comparuou with list IX. are too irregular to 
bo of much ftervic(>. 

5. Magniiiide Equaiion in Photoifraphir. R.A. Gomparistm 
Stars. — III extending to the fainter Httnt our search fur magtiitads 
equation, ire nieel with the tlithrtilty that tlic ma^ruitudes aaitigned 
to these stare at differenL observatonea are discordant. For 
example, on tabulating suvvml huiidrud curnpariHOti hlnrv, we Gad 
that thp ni&gnitu>ics nfMiigiied at Piiris are greater in the meao bj 
i"''6 than thoi<e ii.'UiigiitHl tti the fuinie HiKm at Bonteaux, a,iM 
greater by o'^6 ihmi thow asaigocd to the aame stars on Ciitania 
plat4;«, though these wun.- iijeanured at l^aris. It would eeom that 
thfl Pitris "magnitudes "are really intensities of image on the plate^ 
unreduced Ut any pliotonietric ecaltf ; exc^elleut, therefore, for 
invf-Btijiutint,' iimgnitude equation on platee treuletl iadividnolly, 
but of les« nii'rit when combined inti> lueauH. 

Because uf these discordauces in the luuiigued magnitudes, une 
mtlBt discuss the ditreri-nces — Paris — Bordeaux, for example — i| 
duplicate, onc-e with the Paris tna^itude^ and a second time vrii 
the Bordeaux. Wl- find behnv tin; ckisificution acconlini^ 
magnituilo of the diflureiifo» Pari»— Bordeaux, and also of 
diflerencea Bordeuux — Parin (thn same c]uatititiAa with eigi 
chauged). Thn timt cla46i(ieiition is by ParJH magnttiidea, 
the conipartiiient 9™"9-io'"-5 contains 17 stars. The secor 
division is by Bordeaux niagnituded, and the Kanic couipartmi 
oontaina loi stars. A rvsult still wore curious occiini in 
comparison between PariB and San Kernamlo. Tho last groul 
iz'"'3 and fainter contain)^ 15S stars in the first classification 
Paris niai*nitmles. On repealini; it with the San Fernando magDi 
tudes, all but two of these stars are thrown back into precedii 
groups. It is clear that there will be dilficulties in cxprvaniiig 
error as a function of the magnitude. 

6. The resnlts here discussed cover nearly the same stretch 
tlie planet's jiath as does list I. of the r^tp^re stars, and depei 
largely, thoiif^h not entirely, upon stars common to thti Paris 
other sei'icis. The comparison is therefore ciiomewhat incomplnt 
Quite early in the work it was realised that definitive correctioi 
could not be derived from this material as it stands; that 
sfaootd have to repeat the ubole work in greater detail, nnd tht 
it was not worth while to spend time in making tho pieoei 
preliminary discussion ubsoluttly coraplc-to. 

Phol.ograpliic places of comparison stars have been ]iubli«h< 
in Circulars 10 and 1 1 by Paris, Bordeaux, Catania, San Fernand( 
Toulouse, and Alf^em. Each one of these six observatories hi 
been compared with each of the otlierv. But it is hardly nect 
to give here all the results. It will be sntlicient if wo give t] 
comparisons of Paris, San Fernando, and Algiwra with one anot 
and with the othen. 




Nov, 1906. The rhotographic Places of iitays. 



75 



Tbe first sel shows that there is uo serious dificonlaiico bclweeu 
Paris and others, with the exception of San Fernando. To nee if 
the apparent inagiiitude equation in San Fentatuln in real, we 
compare it with each of tlte others. They are unanimous ia 
sliowinft a relative niagaituJe eqiiatiun, a{){>ruxitDati.>ly linear, of 
about o*.oo9 |>cr magnitude-. Hut we must notice thnt this is of 
opposite sign to thnt snepect^d in the reyt^re stars. Wa shall 
Hftom to this jKinl in |j 8. 

Tlie comparison of others wiib Alpers shows that the extra- 
«irdinary niagDitudo equation of ih*; ritjn-re stars is maiiitiined 
throngb the fainter magnitude^. Kor stars nf the sixth magnituda 
the Algiers KA. is small by about 0*03 ; for the twelfth magui- 
tnde it is large by o"oS — the whok- ran){Q equal to about 1". 



^H 




Tattle m. 




^^^H 


^H Comparison Stars 


Ma^tude Eqaatton in Pbotograpbtc RA'i. ^^^^| 


^H 


Paris minus 


- 






■ 


^H 


Bord. 


Cat 


S. Foro. 


ToiU. 


Alff. ■ 


^^H 


■ 


1 


t 


• 


■ 


^B 


(9) - W) 


(14) -r '016 


(30) + -009 


(21) + xat 


(20) - -005 H 


^■9*3 - 


(«)- 10 


(141 - 3 


(14) - 5 


(17) - 9 


06)- 33 ■ 


^■9*9 - 


(17) - 2 


<24)* 6 


(46)+ g 


(SO) *- 6 


(42)' 32 ■ 


^Hd-6 - 


(36) + I 


(731 - 2 


(7«)+ 12 


(79) 


(70 - 48 ™ 


^Hi-j - 


(56) - I 


053) - 4 


(139) + 2J 


(129) + 6 


t'05) 67 


^Hst'i - 


(93) - 7 


(•53) ^ 2 


(158) t- 2t 


(148) 


tlio) - 88 


^H Tcrtsls 


U19) - W>4 


(431) r-OOl 


(45S» + '0*7 


(444) + -002 


(344) - -036 _ 


^L 


Baa Fanaado minus— 






1 


^H 


Bord. 


Cat. 


Paris. 


T0III. 


A^ff. ■ 


^^F 


ft 


» 


• 


• 


■ 


H 


(28) - 007 


{50) - t»i 


(91) -ooS 


(98) - 004 


(93) - 'D31 ■ 


■«*3 - 


(39) - >a 


C50) - 16 


(68) - 14 


(6S) - 8 


(fir) - 68 ^ 


^^9*9 - 10*5 


(72) - 20 


(113} 21 


(113) - 17 


(109) - 15 


(loj) )i6 


lo-* - n'2 


(S7) - 23 


(112) - 24 


(t35) - 21 


(96) - 12 


(74) - 9* 


11*3 - :2*i 


(t6)- 39 


(32)- 37 


(46) - 34 


(38)- M 


(24) - roS 


■"- 


(0- w 


(1) 4 40 


(2) - 39 


(4)+ 2 


(3) ~ 138 ■ 


^1 ToCalf 


(«3) - 1019 


(357) - *'9 


(4S5) - "017 


1413) - 01 1 


(356} - '072 H 


■ 


Algltrs rainni- 






1 


■ 


Bord. 


Cat 


Paris. 


8. Fero. 


TML ^1 


H 


■ 


• 


■ 


■ 


■ 


■ 


(25) + -023 


(40 +"031 


(76) ■>■ "022 


(79) + -032 


{S^)^•026 ^ 


■9*3 - 9-8 


{3'>+ S7 


(40) + 63 


(63) + 50 


(59) + 60 


(63) + 54 ^ 


H9^ los 


{26) ^ 63 


(37)* 83 


(40) -4 62 


(46) 4 66 


(45)+ 57 ^ 


10*6 - tl*2 


(42)* 66 


(72) + 79 


(76)+ 69 


(86)+ 9S 


(84)^ S» M 


^jj lai 


(39) ^ 73 


(391 + 87 


(81) + 77 


(80} + 96 


(85) ^ 8a ^ 


■.■>- 


W-*- 30 


(5) + "2 


(8)+ 89 


(6)+ 90 


(10) -^ 88 


^1 Totnli 


(IJS) +x63 


(234) + -071 


(344) + 'OS* 


(356) + -071 


KTfXs^-^hi. ■ 



76 



Mj' Minks, Solar Parallax Papers, No. 5. LXVXL 1, 



Tobks similar to tite above for DorJeaux, Catania, and 
Taali.>aHB sbow few fi'uturts of mtert:Bt. For Bordeaux mlxiuf 
others, the nutnbere fall sliglitly to tbe thin) group, ami rise ag^in. 
For Catania and Toulouai! there ta a sltght upward tendency at 
Irbe beginning and end. But the whole range is smaJI, ftquivtileiit 
to abuut o' 2 ; uud, in light uf whut ■will follow, we cannot 
attribute it ti> ma^nitudi:- e^ualido. ^H 

7. Magnituiie ICquiUi&it in Photographic: Declinations. 0(m^^ 
l>arieo/t Stai-K — The procoduTi- fullowcd in di^ell«illg the B.A.'« 
has l)eeu repeated Ebr the declinations without change. A 

:tioD of the more iiit*3r<!«ting results is ^iveri in Table IV. 

Paria, Bordeuux, and Ciitatiia agree fairly well. We can 
hardly look upon tho diflerencos l*ai'i*) - lk>rdoatix as significant 
of magnitude equation until we have examined the eiTecis of the 
difference of adopted places in Bordeanx, which is a very iucom- 
pletti berivs. 

Totilouse diverges strongly from those three accordant aeries, 
and haA a. well marked nearly linfar magnitude equation in the 
declinations of compiirison st-irs of about o"'! pi-r magnitude. 

8iin Fernando ia a dithcult case. We may snmmarii^e thua : — 
Paria —San Fernando (P. magnitudes) shows a very slight M.E, 
lV>rdeanx — San Fernando (It. iua;,'iiitude8} showe decided M.E. 
Catania — 8an Fernamlo (0. ina^'iiitndofi) hIiows targe M.E, 
«if more than o'l per magnitude. 

On the oth(^r hand : 
San Fernando— Fari»i (S.F. magnitudiw) shows no At, 

whatever. 
„ — Uordoaux (S.F. magnitudes) shows none, or, 

most, tniC4-a of a non-linear M.E. 
„ —Catania ('S.F. luugnituduH) ahows a very v 

and uncortaiii M.K. 

The diacordanct.* Ix'tween the campuriiioiis Catania- 
Fernando iind San Fernando - Catania, tlint is 10 a^y, between thV 
figures grouped diflVirentJy ai^cording hs one acrept<t the C'ttania o: 
San Feranndo ungnitudes, shows thut no dehnitive correctio 
can be derived from the pretuut work. Tbt* uia^iiiitude equatio: 
if any, is doubtless entangled mth other systoniatic errors o 
Catania or San Fernniido, fnr which see later, § 14. 

<Vlgiers shows a considerable ma^faitude equation, as befo: 
but it is not nearly eo variable in the faiuler niagniludea as in tH 
brighter. 



Nov. 1906, The Photographic IHacea of Stars. jj 

Table IV. 
Compariion Stirs. Hagnitnde Equation In Fhotograpblc Declinations. 
Paris minns— 

Bord. Cat. S. Fern. Tool. Alg. 

- 9-2 (8) +-03 (14) -'-03 (21) -''09 (21) +"11 (20) -"04 
9'3 - 9'8 (5) o (14) - 5 C14) + 22 (19) + 28 (18) + 22 
9-9 - 10-5 (18) + 2 (25) + r (47) + 24 (48) + 28 (42) + 33 

10-6 - II-2 (37) + 9 (72) + 3 (78) + 20 (81) + 29 (68) + 29 
II-3-I2-I (59) + 12 (153)+ 2 (138) + 30 (126) + 37 (103) + 39 
12-2 - (93) + 4 C152) + I (157) + 28 (149) + 45 (93) + 46 

Totals (220) + -07 (430) + -oi (455) + -26 (444) + -36 (344) + 35 

Ban Famando minns— 

BoTd. Cat. Paris. Tool. Alff. 

- 9*2 {29) - '10 (50) - '15 (93) - '24 (97) - -05 (93) - 03 
9*3 - 9* (38) - >3 (52) - 13 (67) - 25 (69) + 4 (61) + II 
9-9 -10-5 (73) - 24 {110-25 (119) -23 (108) + 14 (loi) + 18 

10-6-11-2 (59) - 17 (113) - 29 (129) - 30 (98) + 16 (74) + 23 
II-3-I2-I (15) - '6 (31) - 24 (45) - 25 {38)+ 7 (24) + 25 
12-2- CO - 20 (I) - 10 (2)4- 7 (4) + 7 (3)+ 4 

Totals {215) --iS (358) - -23 (455) -'26 (414) + -08 (356) +13 

Tonlouse minus — 

BoTd. Cat. Paris. S. Fam. Alg. 

- 9'2 (21) -'-'ll (45} -'20 (S2) --22 (74) +'-05 (77) ''00 

9-3 - 9*8 (32) - 18 (44) - 21 (74) - 31 (70) - 5 (65) + 8 

99 -'O'S (72) - 32 (129) - 29 (129) - 35 (127) - 16 (112) - I 

IO-6 - II-2 (55) - 35 (98) - 35 (123) - 42 (113} - 8 (94) + 7 

Ii'3-i2-i (12) - 61 (15) - 28 (36) - 56 (30)- 9 (20) o 

12-2 - 

Totals (192) - -30 (331) - -29 (444) - -36 (414) - '08 (368} + -03 

8. Summary of Rastdis for Photographic Magnitwle Equation. 
— We may now bring together the reaulta for tlie repere and 
comparison stars. 

Regrouping the reph-e star? into lar^^er nmgnitudo groups, to 
avoid the roughness due to paucity of numijers, we havt- the 
following table for the comparison of Tiiuloiu-is, Alijiers, and San 
Fernando, in which magnitude equation is discovered ur suspected, 
with the mean of Pam, Catania, Bordeaux, in whiclt it does not 
appear. 



78 



Mr Hiiiks, Sdar Parullax Papers, Xo. 5. LXVlf. x. 



Table V. 
CoUaclfld BviulU for Kagnitude Equation. 



HA. 


Tonloose miixui 
■wttof P.CB- 


San Fernando mlaus 
Mean of PC B. 


Alffiers minna 
Mean of F.CK 


m 


B 


a 




» 




- 74 


+ 001 


-o-ois 




0-031 J 


75- 84 


Q 

■ 


10 


• 


- 


« . \ 


8-5- 9-2 


+ I-OXWI 


2- 


0-005 


+ 


i4'*-o-03S 


9*3- 98 


5* 2 


+ 10- 


14 


+ 


'3+ S 


9*9 - 10 "5 





- 


19 




+ « 


iO'6- 1 1 '2 


7 


- 


23 




+ g 


11-3- 12-1 


6 


- 


33 




+ 3 


12-2- 










+ 1 


Ctad. 












7 "4 


+ 0-22 


+0*14. 




■f 


•38 


7 5 - S'4 


+ 5 


- 4 




+ 


« 


8-5- 9-3 


Q-D-18 


6- 


O't^ 


- 


2-o"i6j 


9*3- 9-8 


- 15- 33 


18- 


17 




16- S4. 


9-9 lO's 


- 32 


- 


24 




jS 


10*6- 11-2 


- 37 


- 


85 




" 3 


irj-iJT 


- 48 


- 


22 




"4 


I2'2- 




■•> 






- n 



i 



The firat of the two columnti belougiug lo each ohservatory 
deriverl frnm the repttre stars, the f;e<^on(] frnni tln' i^oiufturiBoii' 
stars. The rou^'huesa at tlie imiiits whem thof^o uvi-rUp nci?d tic 
be taken too seriously. ff>r the miij;nitudes of t\m first are Tucker'^ 
roagnitudoa, i.e. practically B.D. ma.L^uitudef, while tiiose of (I 
aecund aru ph<tUij(ra|>hi(! iimgiiitiidi')?. 

The conclueions, in brief, are as fnlluws: — 

ToulitiiRd has very tittto iiMguitudo (T((ii»tion in R.A., but »1 
largit out; ID declination, which is nearly linear. 

Algien boa a vi>ry lar^e tmngiii tilde uquiaiuti in butb co-J 
ordtDat«« ; larger in K,A. than in r)t>cl. ; not strictly linear ia| 
either, but altering little for the faintest atartt. 

San FenianJu appears to have 11 fairly smiill and decidedly tioi 
Itoear magnitude? i?qufttiun in both co-ordinates. 

Ill e»itimatiiig the! weight of these cnDcIntiiuns we must remeonl 
that there are other KyHtnmatic errors involved with the maunilu^j 
i-qiiaiion, whii^h huve not yet been discussed ; and that tin- . * '^ 
quantity upon which inaj^iiitnde equation muat depend ia lilc' 
be the uuiuber re|irosenting the intensity of tbo in]H,'Jc iip-i 
plate, rather than Uie nnniljer more or Ilkk rfiilnccd '■ 
aoale which is derived from it and published as tb' 
magnitude (except apparently at Paris). For tlip 



Niiv. 1906. TVt*: Photot/rttphic Placa of Starti. 



79 



I 



I 



ftttempc will be made jtut yet tn determiite a f>et of definitive 

corrections. 

9. For the same ivatiouti it la pretaature to allompt it* settle the 
qiieBtiuii — What is the cau»e of these erroMl Hut we may note in 
paatinu;. tlmt at Toulouite and at Algiers tln^ plioto^ruphic equatorial 
is oiountBd iti the " En^liwh " stylo.* so tliat errora of tlio objw;tive 
are not n-versed on croseinj; the mertdiftti ; whila the plnti^s are 
D-'verited during raeaaurement. One will in this case naturally look 
first fur the errur in the objective. At San Fernaniiu the plates 
are not reversed during meosurbmcnt, and the 8iiiall noti-Unear 
magnitude equation may very well he due to this cAHRe. 

Fo. Proffrexittce Dtseotylawe^. Re/t^.re Star^t.—U a phutoxraphic 
tele9Co|»e gives results which are sysieoiatic-jiUy wrong over a long 
Keric8, there is naturally u Htrong probability that the vauoe is 
instnimentiil ; and if ««, the etTt>ct will mmit likfily he a function of 
the magnitude. We have therefore dealt with magnitude r^quation 
first. 

We havo now tit louk for diacordances of a aeiui-syHtematic 
character, varying from ptiint to point along the path of the planet, 
— euch clismirdaiice*, for example, Hs might be due to nmghrieM in 
tha adopted places of tlie rep^-re stars. We will look for them 
first in till! concluded photographic pluceit of the reprre stars 
tlioaiselves. 

E&ch rvfti^re star hail been asatgned to one or other of a series 
of gi-ouj>soti centres 3' apart along the orbit of the planet (alternate 
cuntrvs of list given iir Paris Circular Xu. 3, p. 7, for the " special 
aeriea " plates). 

II. Consider in the tirst placv tho olwervatories which have 
redtioed to a common fimdnniental system (that of M. Loewy), 
vix. Oiitania, (Ireenwich, I'arisi, and Toulouse. The group meAns of 
tho differences of these seriea are given in the table on the next l*age. 

In .studying this table we lUiiHt remember — 

{a) That t,he Greenwich plntM were reduced first of a[l to an 
independent syAtem, and afterwards mean corrections were applied 
to each plate to reduce to Loewy's system. 

(f/) That the Touloune »yt*tcni in not exactly the tiame aa 
I/jewy'a, though for present purposes the diftereoce is insignificant. 

(e) That the platea taken at Catania were measured and reduced 
at Pari^ and ought to be particularly concordant with the Parid 
plates. 

Oi) That the Tolouse declinations are slightly atTected by 
ignitude equation. 

(a) That ^.tar?. ;ip|>eariug in the same group are not necessarily 

■CM with th<- ^^iime selection of reptre stars, or even with any 
• t'l -liv two reductions. 

UiU information 10 the directors of the ob»«rvKtorie» 

a liille otirioiifi thnt, a]thoiigti tlio astroitrspbio 

t work fiir iiftven yosrv, one cannot *lwiiy» tind 

t ti'iuiitiDgeniploytfcl. Yet the iiiicftion 

<1 nu crossiiig the montljui iit funda- 
«mr. 




f 



Mr ffinks, Solar ParaUux Papers, Ko. 5. ucvil i, 



(/) On the othflr hand, that the dimti |>hoU)gmphic place of 

one star will often depend uii a considerable renge of refiire stan 
groupud on differetil centreti, iind thnt Lht* erron of indiridtul 
adopietl pliicvs will be smootbed out uiuch uiuru ctfcctuall^ than 
is the Mi&^ (111 Astrojs'raphic Catdo^e pIaL«N, wuh their eoutrea al 
untfiirm distances. 

fiuaring thf»u factti in mtnd, we may draw the following 
conclusions fraui Table VI. ; — 

(i) The wj'BtKmiitic diflfereiice between Paris and Greenwidi, 
taken over tho whule axrius, is quite iuscuitible. And we foond 
that there waa no trace of relatiTe magnitude equation butweeo 









TaUtTI. 








Bep^re Stan reducsd to tioewy's System. 


'rogTeasiTe Diicordancei 




Paris minus 


— 










Nitre. 


I)*t«. 


Oreenirich. 


ToQloua*. 




C&tanU. 


6 


1900. 

Oct. 2 


(ll) -000+103 


(11)+"- 


005 + 


»5 


()I) - -00t-f-'03 


8 


.. 8 


(15) + 


3- a 


(17) + 


4- 


1 


(171 +30 


10 


.. 14 


(II) ' 


13+ 4 


(15)- 


7 + 


8 


(13) + 22-f ao 


13 


.. 19 


05) 


0- 3 


(ao) 








(14)- 3^ 3 


14 


.. *5 


(IJ) + 


I 


('3) + 


6 + 


4 


(13) + 26+ 6 


16 


Not. I 


ixA) + 


13+ > 


(17) + 


3- 


1 


(16) f n + 10 


18 


.. 7 


(•6)- 


9 


(31) -1- 


2- 


1 


(31) -6+6 


SO 


.. 14 


(16) + 


3- I 


(19) + 


16+ 


7 


(13) + a+ 1 


32 


.. 31 


(16)- 


7^ 4 


[!■&)- 


4 + 


4 


(13) - 8+ tS 


14 


.. a? 


(>5) + 


3- I 


(16)4- 


5^ 


3 


<n)+ 17+ 31 


s6 


Dec 3 


(7) + 


4- 31 


CS) 


i 


3 


(9> + 21 - J 


38 


.. 9 


tn) + 


5+ 4 


(11) > 


2 





(3) ■*- 46-41 


30 


.. M 


(6) + 


3+ 5 


(7) + 


»5- 


30 


(5)- «- S 


3a 


.. 18 


tl4) + 


4+ 6 


(14) + 


4 + 


3 


(6) + ai + 44 


M 


M " 


C16)- 


S+ 7 


(16) + 


1 + 


3 




^ 


.. afi 


(16)- 


4+ 2 


(«7) + 


3- 


S 


(I)- iS+4fl 


roftard to t\ffi 


*oa48 "040 


"0048 '048 


■ « 
0137' -141^ 


Mean 


■0000+ 'm5 


4 -0033 + -072 


t 0060 -t- -oW^ 



Abfa, — Th« averayvB srii fonncd from tlm fcmnii meHtis givm nlmw* 
s<tRii:tiiiir-i Uie Minx star ol-cuth in two t{i'<>ii|>H. Tlirtp il )| 

bir«a i-iimitg«(i befarv the final idcriiw wvra t«k9n, in vii 
reckoiifiu more thau oncH. 

them. We may provisionally adopt t 

Parte — Greenwich as. indic»itive i>f th<. 

* Or, omitting th« loAt foot, which de[MnJ 

an 0-0109 o-o8x 



Nov. 1906. The Photoifraphic Ptaeea of Stars. 



81 



may be reached hy two serieB made iiidepentlently nritb diirercot 
instruments and reduced to the tiiiiue stauJard. 

(2) Tlie divorg.-iices irvm ci-ntre to centre Heein lo tie due more 
to tbe roiighneas nf the rtji^re star jilnces th«n ti> errors nf measure- 
ment, nr real errors of the (»hotogmiih*. Tlii« nmy be seen in the 
columns for I'firiii — Toulouse. Tlie Toulouse pLateit are few in 
number cuuipand wiih Greenwich aud Paris. But the average 
discordance of the groujjs is uearly the saiuo in Paris— TouKmse 
aa it is in I'uris— Greenwich. 

(3) The Catania platM are itill fewer in tiuniber, l>eing practi- 
cally uuly tOternato plalett uf the !>{i«cial Dt-'rieM. Although they 
were meaaurod and re4iucL'd «t Paris, the dibi;onlnn(;o« fruiri PfiriR 
are larj^e. At lirst sight this might ho uttribiited to small iitimbet- 
of plates ami want of averaging out errora by overlapping. But 
the (iiscordaita-H aeem to he too large for auy such simple explutia- 
lioii ; uotice esiwciiilly centrea 10, 14, 24. and z6. Wo will 
poetpone discussion of them till we oouo to deal with the fainter 
stars. 

Table Til. 
Kep^e Stars not rednoed to Lonvy's System. Progreftslve Diflcordanc* 
from Paris of Photographic and Adopted R.A.'b 
Faris minus— 



» 







San Fernando. 


Northfleld. 


Helsliigfora. 


Cmtn. DUe. 


riioi 




AOopt. 


Phot. 


AJoj.1. 


Phot. 


Adopt. 


6 


1900. 

OeL 2 


I ■ 
(11) -f XX}4 + *009 


' 


( 1 


1 


.-- 


B • 


8 


,. 8 


(17) + 


13 + 


6 


{13) +■ 


019 + •005 


... 


... 


10 


.. 14 


(IS) + 


3 + 


9 


(H)- 


1 + 


a 






13 


.. >9 


(20) + 


10 + 


10 


(1SI + 


13 + 


9 


(8)+' 


008+ vto 


14 


,. 25 


(13) + 


9 + 


IE 


(10) + 


10 + 


S 


(9) + 


33+ 10 


1« 


Kor. I 


(>7) + 


M + 


IS 


(<0 


+ 


10 


... 




18 


.. 7 


(") + 


15 + 


IS 


(14)- 


1 + 


11 


(18)- 


3+ 9 


ao 


.. 14 


(19) + 


31 -f 


9 


(n) + 


3 + 


7 


(4)- 


13+ 10 


22 


t> 21 


(r8) + 


'3 + 


11 


(10)- 


3+ 


6 


(13) + 


7+ II 


44 


*» 27 


<iti) + 


It f 


II 


(u)-*- 


16+ 


8 


(15) + 


334- 17 


26 


Dec. 3 


115)- 


1 





(IJ) + 


•3 + 


II 


(»3) + 


25+ 14 


as 


n 9 


(n) + 


5 + 


8 


(8) + 


3 + 


8 


(13)^ 


18+ 13 


k. 


M M 


(?) + 


5 + 


3 


... 




... 




... 


■ 


BmI 


,(14)4 


5- 


I 


(n) + 


3 + 


7 


... 


... 


■ 


^^^p 


ifit,)- 


3* 


S 
3 


(Ml + 
(II) + 


4 + 
3 + 


4 
6 


(") + 

(12) + 


94- 10 


■ 


■ 


15+ 8 


■ 


H 


^^H 


b 


xxyjii 


+ '1 


0057 + 


■0075 


+ «l30-(-'0II2 



dc from Table VI. that it ia poaaible 
''_A.'a and declinations, from two 
.obecrvatorieft— witness Parii 



82 



Mr ffiTtks, Solar Panzllax Papers, No. 5. LXru. I, 



ami Greenwich ; bat even onder conditions which should make for 
accordance, onu finds discurdances unexpectedly big, as in the cut 
of Catauia. 

13. So far we b«ve dealt with seriea reduced to the aame 
fondamental sjBtem. We must now txamine haw far differeoce 
of adupted Hyjilem is likely tu prudii<:e discurdance. 

Wo will take as uxmiiiilex Siici Ftirnando, Northfiirl.l, and 
HeUiitgfors. The comparison ul K.A.'s, both deduced and adopted, 
is given iu Tablu VII. 

It will be seen at once that the difference in the adopted places 
is reflponaible for tbe |>rinci[)al part of the difference in th*f cou- 
cluded pholu^^ruphic places. At San Fernando and HeUingfon 
the lat-an differencL' is i-xuclly iiccouuiwi fur. At Nortliflyld the 
agreement is Less SAti»factory, but the series is leM complete. 

13. The dectinattonx have Leeti treattrd in tbe itanie wav, and 
j;ive a verj' similar result. The mean discordances of the photo- 
graphic declinntions are duo ulmout eutiruly to the difference o{ 
adopted places. 

I thitik we may condade thai the policy of allowing any 
obaervatoty tu make its own system of adopted places far the 
THpi-Td sttir« hail led to well-marked sysUjmatit: diHcordanoea 
between some of ihr pbntogmpliic series, of tlie order of o*.oi and 
o'.i, which it willi \tv Wiirth wtiila t>r eliminate. 

14. OompaTi^ftn Slan. Pi'Ofjre»sivf' Discardanceg, — We haT« 
now to examine how fur the photographic [itiices of the fainter stars 
ditTer from ceutru to centre. Our umlerial in the same as ibut dis- 
cusaed above for in-Hgnitude equatitui. Kach observatory htm been 
compared with each of theotbers. The romnlta have been studied Viy 
plotting in cuivea coloured tu indicate the ulwervatory of origin. 
These cannot be repriHiuccd, mid tbt*' tuUes which represent Iheni 
numerically are nut ijuite successful in showing up the ftiatiires 
which are conspiinmis in the dmgninis. Wo can give only a few 
example!!, and a general i^tateniPtit ff results. 

A typical section ia tLat travvrsed by the planet betwec 
October 16 and Nuveniber 4, wliicli has been divided, into] 
blocks Iftttered K, I,, M, N» (J. Xible VIII. gives the R.^ 
comparisons. 

Since all these cotupsrisoni are dtfTcrential, it is impoesible 
obtain the actual ern>r of any spries. Uut we sumctimes can get 
very good idea of which is in the wrong. Take, f.ir inslanue, tt 
comparison of Catania with olbers. In block K the Catani 
E.A.'s arc ubuut o".04 Kreater than all thri others; in block L the] 
nearly agree ; in blo( k M they are dqoiil<rt|yj|m in block N tbt 

have risen again; and fall once mor^' ' parvd with tl 

others. I think that wa may co^. je that tl 

irregularity is mainly in the Catu' 

In this way it has been touud^ 
of the degree of syslet 
R.A.'h and declinations, 
no means reassnriog. 





Nov. 1906. 


The Fhotoffraphu 


4 
Platts of iUait, 


J 








Table VIH. 




■ 




CDm|»&rUoQ Bt&n. Photo^nphlc BA. ProgreutTe Dt«conluio«t ^^^| 






aetwsan RMtilts from Dlfforent Obtervatoriea. 


^ 


K. 


Ocr. 16-19. 


Paris - 


Bord.- 


Cat- 


8 Fam. - 


Ton!.- ^^H 




Pari! 


f 


■ 
(14) + "Oil 


■ 
(29) +-040 


• 
(14) -Wl 


(13)+ -001 H 




Bord. 


(14) - ^" 


... 


«S)+ 34 


(t3)- ao 


(la) - 7 ■ 




CAt 


(29)- 40 


(15)- 34 


... 


(") - 54 


(9)- 37 ■ 




a. Fem. 


(14) + 31 


(13) + K> 


(■2)+ 54 


... 


(13} ^ ai ■ 




TouL 


(la) - I 


(11) + 7 


(9) + 37 


(13) - ai 


... J 


L. 


Oct. i9-«3. 










^ 




Paris 




(38) + 009 


(16) - ^002 


(J9) - -003 


(36) ' 1003 ■ 




Bord. 


(18) - -009 




(">) - 5 


(17)- 10 


(34}- 13 H 




Cat 


(16) t- 3 


(10) + 5 




(6)- 13 


(8)- 13 ■ 




8 Fern. 


(19) + 3 


(17) + 10 


(6]+ 13 




(30) - 4 ■ 




ToaL 


(26)+ 3 


(14)-^ 12 


(»)+ 12 


C*o)+ 4 




M. 


Oet a3-27. 














Parii 


... 


(29) - -ooi 


(36) - "030 


(39) - -ooS 


(32) +-OII 




Bord. 


129) -fooa 


... 


(3«)- M 


(36) - 19 


(23) + 15 




Cat. 


(36)+ 30 


(36)+ » 




(37) + 3 


("3)+ 39 




S Foni. 


(39) + 8 


t36) + *9 


(37) - 3 




(28) i 28 




Tool. 


{32) - 1 1 


(23) - 15 


(23) - 19 


(38) - 38 


... 


a. 


Oct 57-3 '• 














Parifl 


... 


(31) - -003 


(38) - -003 


(3a) - *33 


(19) - 023 




Bord. 


(iO+xwj 


... 


(35)+ w 


(35)- 38 


(18) - 5 




Cat 


(38)+ 3 


(35) - « 


... 


(34)- 41 


(31) - 19 


1 


8 Fem. 


(3a) + 33 


(35)+ 38 


(34)+ 41 


... 


(ao) + 32 


Tool 


(19)+ 33 


(18) + 5 


(21)+ 19 


(ao) - 32 


... 


a 


Nov. 1-4. 












1 


Paria 


... 


(30) - 'OI6 


(33) - "M* 


(3l)-1XW 


(33) - 1031 


1 


Bard. 


(ao) + 1016 


— 


(a8)- 13 


(31) + 31 


(21) - 3 


1 


Cat. 


(33)+ 26 


(18)+ 13 


... 


(«) + 30 


(a4)+ 7 


1 


8 F«m. 


(31) t 3 


[21) - 21 


(21) - 30 


... 


(")- 31 


i 


Tool 


(M) ^ 31 


(21) -t- 2 


(24)- 7 


(23)+ 31 


... 


1 


15. Paris comes out decidt^dly the best. Only in a few cases 
- «V8tKniatically diffnreiit fruia all the oth«ri«. 

reaults are oIhu ^ood. Tbu UitTurmicas fnitD utbur 


1 


^^ 


^^rery irregular, nm. 
^B^A to Uordeuux. 


tu be attributed, ia 


hvi iiiuiu 



84 



Mr Sinks, iiolar Parailaz Paptn, No. 5. UCVQ. 1, 



Catania is an extremely interesting case. The discordoncei 
from Parii) ar« quite extraoiltiniu-}'. The following ta}»lc gives 
tbejr valnea in the section where thev are best detflrmiiied : — 





Table IX. 






Comparison Btan. 


FrofrrositlvQ DlBCordaQcn. 




Paris minus Catania 




Uodc 


Ko.9fSUn. 


Mean MtconlfeD^e In 
R.A. l;tci. 


K. 


(8) 


t 


•oij 


-'06 


F. 


{3») 


- 


18 


- 5 


0. 


(12) 


+ 


3a 


- 9 


H. 


(3°) 


- 


ai 


+ 24 


K. 


(»9) 


- 


¥» 


-t- 13 


L. 


(16) 


- 


2 


- 12 


M. 


(36) 


+ 


30 


■¥ 12 


K. 


(38) 


+ 


3 


- '9 


0. 


[33) 


+ 


2£ 


- 7 


P. 


t39) 


+ 


3 


+ 7 


Q. 


U') 


- 


36 


- '3 


B. 


(38) 


+ 


21 





S. 


(4) 







+ 13 


T. 


(") 


+ 


34 


- II 


U. 


{lO 


- 


40 


+ II 


V. 


(3) 


- 


»5 


- 5 


X 


(7) 


+ 


74 


- 2 



The greater part of the error Ik cui [ainty in tlio Catania place 
It is lots in Decl. than in K.A. It dnen not corruspuiid at nil vrel 
with the rather large discordance Iwtween I'aris anrt Cataiiia ft 
the rept^re stars, and cannot be due to roughness in ilm adopt 
places of tlie etam, for tin; placee wbtrt' it in- greateH are geiierallj 
those where Paris plates aio must numerous. 

t'p tu the prertciit 1 htive not tmcceeded in determiniDK 
fortn of this error, or in finding any ciiplanation of it. That twi 
series of pliit<M, taken indeed with difTt^rent telescopes, bt 
ineai«ured and reduced by the tt&wv hand»^, shuuld give re»utta 
reiuarkally discordant, could hiudiy have been exptcied by tl 
most avowed dinhelifver in the accuracy which is claimed, 
generally witli troth, for the photograpLic methods. 

Toulouse and San Fernando exhibit gnat uud vury • 
divergencea from the others ; but we bavi' idrendy ah 
these wries are aflected by rather large niagnituc*'- 
which in a climate of variable transparent^ inu'^c 
associated with eeini-systematic mean errors uf 'in< 



Not. 1906, Prof. WhUtaker^ I>istrihHtion of Energy, etc. 85 



now considering. The pnly «ure methoi of procedure in «ur,li 
A case saeins to be a discusBion tor ma;<nitade equation plata by 
plate, which la impo«tiiblK> unlcba the published material is amplitied. 

16. Ctmclusum, — The results of lUis discussiou muke it clenr 
that the star places published iti tlie Paris Circulun are by no 
mejiuB hoiiiogetieuiiH, anrl Unit errors exUt in fonw uf tiic series 
vhich, uoeliminated, would ruin tho determination of the solar 
parallax. I havt*, however, ful) contidence thAt tho»e dillicultits 
can be ii^'ercome. By the great kiudness of the dtre<:tor8 of several 
observatories, the sL-pamte resuIU's from each of thuir platoe liave 
recently been placed at tny disposal, anil the discussion of this 
material ia now procewliiig at Cambridge, with resulta which I 
hope to commuuicute to the Society. 

17. But our conclusions have, it eeome to me, an iutcrest vrider 
than that of the particular problem in band. Most of the photo- 
graphic telescop«« concerned have been engaged for years upon the 
Aiitrographlc Chart and Catalogue. With that esperteiice behind 
theni, thoy undertook »lian.'B in the Eros tu-opemtioii ; and several 
of the rettulting series of star places are affecteil by errors much 
larger than are accounted tt>lerable in the .-Vstrographic Catalo^me — 
a disquieting result. 

1 8. The work KummariRed in tliis paper was done concurrently 
with that dc»a-ibt.^d iu paper No. 4, and iho same uckLowlodgincuta 
are dne to tlie (ioveramotit Urunt Fund of the lluyal .Society ; and 
to Mtas Julia Bell, who has carried out the greater part of tbo 
comput'ition. 

Catnbridfft Obatrvatery : 

11906 Ifowmber 7. 
Tbe distribubion of energy in the conttDuous spectrum of the 
'•black body " at various tviuperatures, which Is of intere«t 
astronomically from its application to the prolileta of solar and 
atellar temperatures, has been studied from the ojcperi mental 
side by many physicists, and the results obuinad have been cu- 
ordinuteit into the form i-f empirical laws of radiation. One sudi 
em[iirical law, which is due to Lumuier and Pringsheim,* ami 
closely r.>]!n*!«^ntfl the observations, is to the efff i;t that the intensity 
in the part of the spectrum at wave-length \, radiated by & black 
body at the absolute temperature T, is proportional to 



(*T)i: 



On the DidrihiUion of Energy in the CojUinuou* Sjteciram. By 
E. T. Whittaker, Sc.D., F.R.S., Royal Astronomer of Ireland. 




. . . (I.) 

.w».^ of T ill this formula is not re&lly 
"ored by therniodynamical cotisidemtions 

, 2, ISO, io3-iSo(i( 




86 Prof. }Vhittaker, On the Digtributwn of Lxvn, i. 



that if the energy botween wave-lengths X and \ + dK, when the 
body is at temperaturii T^,, is ^(A.)<^X, then the correApondiitg 
quantity when the body is at temperature T is 

. . . (O.) 



ilPO"^ 



Lammei- and Priogsheim'a formula is evidently constructed to 
natiefy this coni^ition^ am) what is retiUy (^nipiririal in the forninU 
is therefore tlie mode of occurrence of A wheu T is constant ; hi 
other words, the diatribtitiun of ener};y in the u|)6ctrum at eoae 
Olio duHiiito teiiiptiratiiro is taken from observation, and the ilistri- 
butinn of energy in spectra at all other tftiupe rata res can then bo 
deiliiced intm thermndynamical principles. 

For tliu above furmula (I.) no theoretical Justification has jet 
been found. JBub one funiturc, common to it and to all the rivi) 
forniulse which have beon 8U>;gentp(i MiirB the refiuli* of olwervations 
ill the extreme infra-refi liave been available, is that the difitri- 
butioa of energy in the regiun uf lunx wave-lengths is proporlioual 
tv 

TX-*,/A , . . , (Ut) 

In other worda, tlie curve of intensity I in tfae spectrum mut 
approximate to the curve I = CTA~* in the altra-red where C ia a 

constynt. 

This resalt (III.) may now be reganled ah a well-estabUahed 
reatilt of ohservaiion ; * and it becomes important to inquirv 
whether it can be explained on theoretical grounds. 

Seveml writurH imve discusacd this qucisliou by the aid 
assumptions regarding tbe nature of tbf* radiating mechanism 
tho black iKxly. Lord UayUigh f suggested the application of the' 
Boltzmann'Maxwell dotitrine of tliti partition of energy among the 
different modes of vibration. Tlje ditttculty here lies in tbv 
doctrine itself, which i« not free from uncertaiatiei', nud would giv» 
renulta inconfti»tettt with observation if applied to tbe shorter 
wave-lengtbs. 

Planck I has attacked the matter from the point of view of 
distinctive theory of tbu nieL-liani«iu of radiation. The radti 
body is supjioaed to contain a great many eleclriad vibrators, 
huTiiig its own peri'id of free vibration, and exchanging et 
with tbe ffitber and the rual^riul molecules. By discuHsiou 
sucb a sy^jtcm, Plunck derives Uk* law uf radlstion 

^ ffA,' 



% 
»**-i 



' It ia rnrt1)«r confintio! by th« obMrniliaiia of Rii1>*i» 
Ann. d, Phyx.. iv. )>• 649(1901). 

+ "R«ii>urkH iijioij tlir IiHW nf CnmpUtf' I ■ . 
(1900). Lorrl ItavIi?i;;li*H |'*l"-r wt- wrJttoii > 
Men cxperiinaatftl iy vcrilnNl, and tli'M- ' 
from tliMrv. Seealio Jeiinii, i'hii. M 

t Ueber dn* Omi^Is lier Kiivrgiuvi; . . •. 
/■Ay»..iT. 553(igoi). 




ov. 1906, Energy in the Continumi& Sputritm. 



87 



I 



V 



where r-^ and c^ are coTistaiits. This formula evidently satisfies law 
(III.), and t» iiiileed in good accont with ^obftervation for the 
shorter wave-!ength» also. 

Later, Ijoretitz* guve a different view of the mechaiiiBm of 
railiatifjQ : he expUins the emisfion of a metal bj nieanit of the 
heat-motion uf its froe electrons, which are re^'ardtid as muvinf! to 
and fru with a vvtocitv of agitation increasing with the temperature, 
and frequently striking againnt the moierules. He shows that 
such a system would euiit the longer radiations in accordance with 
formula (III.) above. 

The ohjvct of the present [taper is to show that fornmla (III.) 
can he e-Htablished on theoretical ^muiiidA quite apart from any 
assumptions as lo the iiieizhaiiisEn of radiation; that in fact it is a 
necessary consequence of the laws of theniKHlynaiaics, together 
with the usual assumjitions rugiinling the nature of the white lighi. 

Natural radiation is now generally undenitooti to consist of a 
eoocession of diitcrete dirttiirbant^es or " pulsnt " in the atther, which 

not co-ordinated as regards phase, and each of which con>;ist8 of 
cmnpeasatiiiK positive and uo^ative parts, so that th<j curve re- 
pranating a pulse has the total area of those poriions of it which 
Me below the axis equal to the total area of those portions which 
an above the axis. By the agency of a pristn or grating, h single 
pulse of this kind is drawn out into trains of [lertodic disturbances, 
the dispen^ivc uppurulus in fact pcrforuiiii); a resolution of the 
pulse which correspcnde to that furtii^hed analytically by Fourier's 
integral ; and It is this resolution whirb constitutes spectroscopy. 

Suppose, then, that a pulse In ffitlier is represented \ty f{T — ct\ 
where x denotes distance measured in the direction of propaciation 
of the [lulso, / denotes time, and c is the velocity of light in aither. 
We shall express the discrete character of the pulsu by »upposinx 
lbat/Ca;-rf) is zero except when j:- chiles between the limits a and /i. 

Then Fourier's residutiou can be written 

/(« - cl) = i / dn fcos (n{x - c( - m) ]At^)dfL 

IT J J ^ 

So when the pulse is s[>ectroscopicalIy resolved, the elemeats with 
WBve-lea^fth^ between A and A + (/A in a-tlier will be (writing 2v/\. 
for rt, and also for con venieuce writing « + y for fi.) 

'^,^£""cos{^(x-<r<-a-j,) }/ta+i/Kv 

Tow throughout the ran;;e overwhicli the intettrntion is taken, y 

small compared with A if the wave-length is tiiketi so fur in the 

Lbnt A is largt; compared with the extent of the pulsi>. 

yto expand the cosine in ascending powers of -^ and 

ami Abttorptioii )>r Metal s of R«3^a of Hrsfnf gnat 
~» of tht AmMrriltim Afndtm)i of ScUnees (Ki»gli>h 




88 . Prof. Whitiaker, On the LXVtt I. 

retain onl/ the leading terms of the expansion. Retaining for \h» 
present the first two terras, the preceding expremion becomes 



2'fK 2V ■ 

— ^*m 

A- \ 



|?r(,-e<-o)|y|"iA« + y)rfy 



The first of tbeiw integralH vanishes in comequeDce of the condittoo 
that the pulse consists of cotupousating positive and nep«tive purts: 
the second integral depends r.n the particular funn of the jiul^e, hut 
is independent of A, and will in general have a linito value different 
from lero^ which we shall deooto by C. The sirectrgscopic element 
of the pulse with waTo-length)* between X and X + rfA is therefore 

dirOi/X . ( air, , . ( 

Now if in any disturbance the spectroecopic element with wave- 
lengths between X and X.-\-dk is 



it 



y<A).dA.8in|^(*-rf-«)|^ 



it M known* that the energy radiated in this interval is propo 
tional to \'j/(\)}'<?\. S«> in tlie present case lUe entr^y radia 
with wave-lenytli* betwetm A ami A + rfA ih pn'iiifirtional to A"*tf. 
As the varioiiH puUiss are supposed tt> he (entirely unco-ordinatfd 
regards phase, thm law which holds for each ui them individually 
will hold also for Ihvir a^^regate ; and therefore, in ihr railiatiou 
emitted by any body, the energy in tlie part of the spectni 
1>etwc6n A and A-f-i/A is pniportional to A'VA in the region 
longer wave-lengths. 

From this result, by an application of the thtrmodynaniicaT 
theorem (II.) above, wo immedintidy deduce the couseqiienoc 
that the radiation of a Iwdy at temperature T is, in the ultra- 
red, prO|x>rtional to TA"*«/A. 

Law (IK.) i** thus established as a direct cvtnsequance of lh«^ 
nature of white light, witliout reference to the mechanism of 
radiation in the radiating body. 



I 



On the Resuiving Power of Speetroicopes. By E. T. Whittakor, 
Sc.I>., F.K.9., Royal AstroDomer of Indand. 

The resolving power of a a|>ectrusco[>e is, according to thf; neual 
deimition, the value of ^, wherv SA is such that the lu 

cuittre of the ^pnctral line of wave-length A + SA falU on t' 
minimum of intensity of the line of wave-length A. It •' 

* (y. Url Rayleigh, PhU. Ma^.. xivli. 46o(i5£ 



Not. 1906. Beaotving Povxr of SiKctroscopes. 



89 



» 



known theorem that if denot«A the d«Tiatiun of light of wave- 

ff/i 

length X, 80 tlint — nieasutos the disperBJon caused by the 



spectroscope, aud if a denotes the brca>Hh of tlie beam of parallel 
light of the wave-length A as it emeri^es froia the dispersive 

apparatus, then the resolving power of the instniineiit is a -r . 

The reaolring power of a spectroscope can also be discussed in 
couuectiori with i\\e luoderu view of the uabure i>f luiiiiooue 
rdt«tarl>anc'i ns a succo»»iou of puUes. This lias been dune by 
larmml writers. * In the case of the grating, it iff evident that a 

I0 incident pulse U brolceti up into as many separate pulses as 
there are spacings in the grating: these feparabe pulses, as they 
iaeue from the trratitig, are nu longer in the Bauiu wave-front, and 
they will consequenily fullnw each other at regular interi-als to the 
forus of the fih^erviiig tetoiicupc!. In thin way we cau establish 
fur the grating a theorem to the effect that the number of 
ulternatiiJiin, in thu diiiturhance which in formed frnin a single 
original pnUe, i* equal to the n-snlving ])owcr of the instniment. 

The (Vuis of dispKrhion by a priiini present^^d greater difht^ulties, 
as it seemed soniewbat mysterious that altemationa should be 
furraed at all in this caae. But the discussions of Professors 
Schuster and Ames and Lonl Kayteigh t make it ovidt-ot that the 
difTerence lietween the wave-velucity and the group-velocity of 
luminous disturhan<:o in the material of the pritim will cause a 
single incident pul»e to beitpreadout intonn alternating difiturbance; 
and the working out of this idea verifier! the name thcurcia for 
prisms as baa been stated ahove for gralinga, namely, that the 
nuinlier of pulses into which a i^ingle iacident pulse is spread out 
is equal to the resolving power of the itistruuiont. 

It becomes", therefore, of interest to determine whether this 
theorem can be establisliod in the inoHt general case by a proof 
which will bu indepmidL-Eit of the nature of the dispersive apparatus, 
and cont*equently applicablf to every typo of spectroscope. The 
object of the present mite is to nommimtcate ftuch a proof. 

Suppojie, then, that u pulse, which for our present pur|K»e we 
may re^rd as a tiiiri [dune sheet of disturbance moving perpendi- 
cularly to its own plane, is iiicideut on uny di»p'r«ivu iifiparatu*. 
For tiimplicity we jiIihII suppose that the Kourier analysis of the 
piiUe will yield radiations uf wavedengths X and A. + (/A only. At 
incidenu(< the pidee-front, or plane on which the disturbance exists, 
is the same as the pha^-fnmi, or plane j>atatlel to which the 
A-disturhaiice is in the siime (ihase ; but after emergence from the 
rsive apparatus thi8 will no longer in general be the case. 
"■ED, tlut if) deuotvs the angle between the pulse^front and 
euicrgeuce ; and let d6 denote the angle between the 




Sail, Larinor, Rihii^tor, «iid AniM. 
^IS**' P-3^5 ('904' ; Am*i», Attrop/ijftiMlJottnnl, 
' ('905)- 



90 Pro/*. Wliittaker, Baolving Pouter of Sputroscopes, 

phafle-fronu for the A radiation and the X + d\ radiation, _. 

d$ is the dispeniioD. If, now, AC, BE iu tbo fij^ure are .^- 

succcssivt; create of the \-disturbarice at emergence, und A D, BF 



Lxni. ^H 

1. «o thifl 




two RucceASTTB crests of the X + rf\ disturbAnre, then the palse-front 
will pass through the points A,6, where the crcsU roiiiforce each 
other. Thua if AK, AL are perpendicular respectively to RF 
and B E, we have 

AK = A, AL = X4-rM, KAL-rfff. ABKi=^ 

and so from the figure 

ABiin ^=X, ABsiu (^ -t- rf^) = X + dX 
Subtracting these two equations, we hare 
AB cm4>de = d\ 
and dividing this into the first of tbetn, we hav? 

Thin equutioD, which is applicable to any dispersive apparatiUt 
ifhowH that the taexcnt of tlio lm^le between tlie pulse-front and 
the phase-front at emergence is equal to the product of the wmv«- 
lenijth into the di^pernion. 

Since the resolving power is the product of the di8|>ersion into 
the brcudth of the t-uierj^ent buaiu, it follows from this equation 

that the resolving power is equal to the product of _- taa ^ into 

the breadth of the emergent beam, i.e. it is equal to t^e product 

of -^ sin <|b into the breadth of the emergeut pulse. But ~ 

evidently AB in the figure, i.e. it in the interval Vjotween ti 
successive maxima of intensity in the puUe-front ; and ibnn *\ 
resolving power is equal tn the quotient of the bn* 
emergent pulae by the interval between two aucnessi' 
it; that is, the reeulving power is equal to the num' 
maxima of dJAturhance in the emergent pulse-fr 
be proved. 



Nov. 1906. Oreenvnch Ohservaiiotis 0/ Salelliie. 91 

Exitnded NelnUa near 26 Ceti. By Dr Max Wolf, 
Assoc. R.A.& 

On four piaUa t^ken with the Bruce i6-iDch telescope in 
September I fitnl im extended nebula, wliich attracts utlcntbn both 
hy its eituation umJ it^ nppcarance. 

PracticalLy all extended nfihtilostties are found in or nnr the 
Milky-way, but this object is abutit 70* distaot from the pkue of 
the Milky-way. Its densest part ia situated at 

a^gh jym.^ 8„ + J- jo' (1885-0) 

Round this ia spread faint nobulous matter of vaiyiug intensity. 
At «8veral points umall clouds of greater density ehine forth. 
Further out, the intensity is so feBble that it is imposaible to 
exactly delme its limiU. It seems thut these will be nuterially 
altered by leniithening the exptiaure. My expoaiires extend to 
four hours. With these the nebulous cloud ".extends about 40* 
in declination and about 30' in ICA. The three B.D. atars 

h m 

+ I*.I9I a—o 564 5 = -rl'a4' 

I .200 57*0 I 27 

I .2or 57-3 131 

uru all involved in the cloud. 

Southwurda it reuchea nearly to the B.D. star 

+ o''.ao7 o'' se^-g + iV 

but it cannot be certainly detected up to the star. Especially 
towards the west the nehiiloua matter promi-"*);-? Ui go much 
farther. 

Under the micrnscope the brighter parts of the maaa are filled 
with numerous very niinall gpviia and short trails, no that the 
appearance is very different frum that presented by the Milky-wuy 
nebulw. It sooins poMiiblc tliat this object U a uiuUitude of very 
small planetary nebulas collected in a chister, which a more [Miwerful 
instrument than mine may perhaps resolve. 

Aitrophy$icat Obttitatory, Hetdtibtrg : 
1906 October . 



Obtervaiiotu 0/ ihe SaiellUe of A'eptum from P/totwjyaphs taken 
at the Royal Oftiefrvatori/, Oremttcieh^ bei%Been 1905 December 
and 1906 April 35. 

{CammuHuateii by Ike Attranomsr iZoyo/.) 




utraeurcs uf posit ion -an gk^ and distance 01 

Tu mnde from pbnto;hT>tphs taken with the 

^8on equatorial. The ucculting 

The photographs were 



H 93 ObgervtUions 0/ the SatellUe of Neptunt 


Lxvn. i. 


^K Uikeii hy Meiuira Davidson 


I'^ney, 


Dr Melotte, and 


were measurMl 1 


^1 iu a position micrumeier 


in direct and 


reversec 


iKiBiliuiis br 1 


H Mosars Duvidwu and Kdiiey. Ti 


B tabtila 


r posilious with whicii | 


^1 nomparisou ib iimu 


e were 


funjputttd fmiu 


iliti daUi 


given 


in \Xit 1 


^1 LVmrutuiianee du Temps, bnseil nit 


Dr HE^rmtitiii Ktruvti's eleuienb^ | 


^P the eccentricity ot the oibib being r 


eglected. 








^M A (lihicussiotj of tfie^e n^niduaU ^ivi>« Ilia 


foHowii 


u; difffrences in 1 


^^^^ the sense Tabular-* tbaerveil to Dr 


Eiermanii Struvu's 4-leuieat8 1 


^^f 


dN=- 


i"-i6 


(fI-+0 


'■17 (/a=+' 


05^ 


^r tiiviiig for tlie epoch 1906*3 










^^^B I 


6''i8i 


N=i88*-7i 1 = 


= ii6'"S 


1. 




^^ 


Nm-ruse AKi> 


SATK1.LITK. 




' 


^1 Pantion'tat^U and IHatanee from Photoy 


rapha (akifti wUh the 


36 ineA 


Ssfmctar. 


^^L^ D*te will (I.H.T. 


PO!ilUoa-4ugle. 






J 




Oh«ervi;il, 


Tabninr 


T.-O. 


Olwi.rvrd. 


TMbuIftr. 


T.-O.W 


^^P 1905 d h m t 


4 


J 


* 


J, 


^ 


. ■ 


^r iJec. 19 10 5IJ 6 


115-48 


"S'5S 


+ 0-10 


15-02 


'5-46 


+0-44B 


^1 1906 












■ 


■ Jun. 13 It 7 27(ri) 


(45-38) 


45-03 


(-0-35) 


(13-32) 


12-93 


(-0-39) 


^^_ 13 It 35 


42*43 


43 -68 


+ 1-35 


12-46 


12-St 


+ 0-35 


^^^fe 19 12 13 


32-04 


32-62 


+ 0-58 


1 i-Sc 


12-00 


+0*20 


^^H 13 4S 


2973 


3075 


-(■1-02 


12 01 


II -89 


- O'lS^ 


^^^y 22 II 9 


2t3'11 


211 "36 


-075 


1214 


11-92 


-o-:^ 


V 22 1 1 34 27(f) 


»o8*37 


209 88 


+ 1-51 


11 '56 


11 84 


^o-M 


^^^ Fab. 3 7 59 36 


200-43 


20} "90 


+ 1-47 


11-63 


11-43 


-o*ao^ 


^^^^ 3 8 30 


199-21 


200'U5 


)-o-84 


11-35 


11-37 


+ 0-12 


^^H 


19852 


i^ti-tK 


-0-34 


11-09 


11-30 


+ 0-2I 


^^H 3 9 39 S7 


195-oS 


190-34 


+ 1-26 


jfii 


11-24 


+ 0-I3 


^^1 3 95456 


193-08 


19478 


+ 170 


]i-:4 


1 1 -20 


+0-06 


^^H 12 


359*23 


3SS'S4 


-0*69 


lo-SS 


Il'OO 


+ o*ia 


^^^1 12 10 9 sHy) 


356-21 


35690 


+ o'69 


10*95 


II'CJ 


+o-ti6 


^^^H 13 II 7 42 


35268 


353-18 


+ 0-50 


10-83 


11-05 


+o-aa 


^^^H 14 10 2 


245 45 


246-53 


+ j-o8 


1503 


1509 


4-o->o6 1 


^^H 14 10 3) 


244-40 


245-66 


+ 126 


14-98 


15-00 


-^01o^H 


^^H 14 10 54 


243 ■99 


244'69 


+ 0-70 


M79 


I4-8S 


+ OX)^| 


^^H 14 11 


242-63 


243*94 


+ 1-31 


14-82 


14-80 


-D-Yl^H 


^^H 15 9 13 


174-71 


1749" 


•rO-20 


11 06 


11-02 


-0*0^1 


^^H 20 9 44 29 


239-2 t 


240-83 


+ 1-62 


14-41 


14-44 


-hO-O^I 


^^^H 20 10 II 36 


23834 


239-81 


+ 1-47 


14-32 


1433 


+o«^| 


^^H so 11 14 39(/) 


336-88 


237-38 


+ 0-50 


14-22 


14-07 


-<r^H 


^^^ 23 10 36 42{A) 


54*10 


5S'3S 


+ 1-28 


13-47 


I3"S4 


-ff H 


^^^ 23 I' 8 3i(tf) 


5325 


54-08 


+083 


13-19 


15-76 


H 


^^^^ Mu. 2 9 35 30(0] 


326-92' 


327-27 


+0-35* 


II •38' 


11-99 


•^^^k 


fc^_ 




'Halfwtigbt 




^ 


fl 



^^^H 


^^^^H 


■ 


■ 


^H 


■ 


1 


■ 


^^H 


^^^1 


Nov. I 


906. from Photographs taken al Qrte^ 




twuiA. 


95 ^J 


1 


KSTTOKB AND SATELLITE— eO)t/lM«I«f. 




^H 


■ Dab! pn*! n M T 


FratfUun-atigli-. 




tH>Uac«. 


^^1 






Oiweired. 


TkbdlAT. T.-O. 


UbMrved 


l-^nUr. 


Tv^t. ^^^1 


I9D6 d 


I1 m ■ 


, 


* 


• 


IB 


« 


^^^^H 


2 


10 2 6f«r) 


524-I3 


325-85 + I 72 


12-05 


12-09 


^^^1 


2 


10 31 44 


324 '89 


324 30 - 0-59 


12-01 


lZ-20 


^^^1 


3 


10 54 35 


3" 23 


323-1 


3 +090 


l3*IO 


12-28 


^^H 


3 


10 )3 17 


272-44 


27323 +079 


1632 


16-57 


^^^1 


3 


to 46 J9 


271-03 


272-3 


1 +1-28 


16' 50 


"6 '59 


^^^1 


k ^ 


II 15 41(f) 


269-96 


271-50 +1-54 


16 '39 


16*59 


^^^1 


1 7 


9 SO 59(r) 


42 14 


4: -69 -0-45 


1273 


1249 


^^1 


1 7 


10 18 z8(e} 


39-38 


40-33 +0-95 


12-27 


12-38 


I ^^^B 


P 7 


10 44 20(*) 


(14 "29) 


39"03 (■^4•74) 


("•54) 


12-28 


(-0-26) J 


^ 7 


11 13 13 


36«5 


37 '55 +070 


12-11 


12-17 


+ D-06 ^^^1 


12 


837 32 


87 -ss 


88*49 +0-61 


16-84 


16-50 


^^1 


13 


9 6 27 


86-84 


87-68 +0-84 


16-65 


16-4S 


^^H 


IZ 


9 47 *4 


8573 


86-53 +0S0 


16-97 


16-45 


^^1 


22 


10 25 30 


19230 


I94-89 +2-59 


11-03 


10-96 


-0*07 ^^^H 


23 


10 so 41 


I9»73 


19332 +059 


11-03 


10 '92 


^^^1 


29 


9 w> S3(» 


1 1324 


114-16 +0*92 


1471 


14 -88 


^^^1 


29 


9 50 37(/) 


in"o6 


113-17 +21' 


15-16 


'4-99 


^^1 


Apr. 3 


8 38 4'W 


178-90 


179-05 +0-15 


ti-io 


10-70 


^^^H 


L 3 


9 5 39<'<) 


176*3' ■ 


177-32 +roi* 


1077* 


1071 


-O-06* ^^1 


1 3 


9 36 35(0 


174-96 


175-3 


1 +0-35 


1097 


1073 


^^H 


1 3 


9 59 320) C'69'So) 


173-84 ( + 404) 


(11-50) 


1075 


^H 


l_H 


8 S 17 


109-36 


1 10-7 


5 -^ ' '39 


15-11 


15-18 


+0-07 ^^^H 


^K4 


8 41 K 


108-17 


10970 +1-53 


15-21 


15 28 


+0-07 ^^^1 


■4 


9 7 7 


10693 


108-S8 ■4-t-9S 


1522 


15-36 


^^^1 


4 


9 31 40 


107-38 


108-11 +0-73 


15-24 


'S'43 


^^^1 


6 


8 2 7(0 


355-38 


355-69 +0JI 


10-42 


10-70 


^^H 


6 


831 33 


35a '96 


353-80 +0-84 


[O75 


10-73 


-OX>2 ^^^1 


6 


9 4 38 


3533' 


331-68 -o-Si 


10-72 


10-76 


H-O-04 ^^^1 


6 


9 3* i» 


35' -09 


349-67 - I '42 


I07S 


io"8o 


4 ^^^H 


9 


8 a 57(A) 


169-98 


169-96 - 0X)2 


10-67 


1077 


^^^H 


9 


8 38 56 


165-97 


167-68 -H-?! 


10-97 


10*82 


^^1 


9 


9 8 I2(«) 


I65-54* 


16586 +0*32* 


10 -99* 


10-87 


^^H 


10 


8 1336 


'0334 


105*12 +1-78 


15-50 


1564 


+0-14 ^^^B 


10 


8 40 550') 


103-50 


■ 04-0 


+0-51 


'5 '53 


15-68 


^^H 


M 


9 a' 33 


23479 


235-96 +I-I7 


13-79 


"352 


^^^H 


19 


84948 


275-68 


276-44 +076 


16-09 


16-07 


^^^H 


35 


8 S3 S9(/) 


269-34 


271-4 


+ 2*17 


l6'Dt 


16-it 


^^^1 


la) Iniftge of SatellitB 


itn perfect 


. 


{b) Neptune near edge af shuttt-r. ^^^H 


[r) [>ifliifl«d. 






{d) Very diffuaej. 




^^^^H 


(c) lilxtrcnitlr liilTiimfc 


. 




{/) F«inl. 






^^^^1 


ly) Faint 


n* 






(A) V.ry f 


lint an<l diflhsed. 


^^^^1 


U) Eltntr 






[k) SatftliU' toiK'l 


tiiu (rinire of ^^^^| 


I 








wwoud*ry j-pcclrunj. 


^H 


^n 


■r 'tF::^ 


wM 


^^ 


^ 


^ 


^^^H 



ucvaM 



94 Qreaivnch ObaervtUwns of Comet c 1905. 



Ofwrmtion* 0/ Comtl e 1905, //»m Photograpiu taktn teitli thi 
yy-inch Rejlector of the Thompson Equaiorial, 

{CommHKicaUd bjf the AArvnomtr Atyo/.) 

The followiniii pnaitiima of Comet c 1905 were obtained from 
photo(frA|ihs tnkeii witli Uie 30-inch rcllectur. 

£x(>OHurcs of 4'" ainl 5" wort' givun on December 8 and 9, from 
i" to 3"'' on Decemtier 19, ami ^"^ for the remainiier. 

'I'he plate;* wer« tncaitur^ iti the axtrograpbic micrometer. 
Sis Tofereiice attirs were tuken wlierc possible, situnted as sjis- 
inetrically aa pussiblo aLuut tliu comet. The [lOfitiunH of the 
stars wr-i-e taken from the catiilogHM of the AstronumiBchp G*well- 
Bchftft, ftr from KarUruho Obaervationit i88s'o, or the RadrltfTt 
Catalogue 18910. 



1905. 


A[i(Mrant K.A. 


AiipAniiL [)u«l. 


LobA- 


CoTT. tar FmMmOMx. 


K.A. 


Ded.' 


d h m t 


}\ in ( 


• 1 II 




u 


■1 


K. 8 17 12 41 


14 31 18-99 


+ 20 5 4-6 


0'I47S 


-0-25 


+ 4-0 


9 17 S 3 


14 36 to'66 


f 19 36 56 7 


01 409 


-035 


+ 4-1 


9 18 7 51 


14 36 23 48 


-t 15 35 45"* 


0*1409 


-o-ai 


+3l 


19 17 30 37 


15 30 26*34 


+ 13 46 40'o 


00903 


-0-27 


+ 4^ 


19 17 S** 6 


IS 30 33*'i 


+ 13 45 5i"S 


00903 


-o-aj 


+ 4* 


1906. 












n. 6 iS 40 i? 


17 34 40*56 


- 3 10 49-3 


0-0425 


-o-as 


+ 6-J 


7 i5 46 S3 


17 42 39 12 


- 4 21 40-3 


0*0435 


-0'2S 


+ 6-4 


9 18 46 6 


17 58 56*0 1 


- 6 46 9"6 


o-044» 


-0*29 


+ 6-4 


10 18 39 27 


18 7 16-25 


- 7 59 46*0 


OT04S7 


-0"29 


^1 


iCVyoJ Obaerraiorti, Oremwich : 
1906 J>/<»Kmbtr 9. 








J 




^^^^^H 


^^^S 


^B 


mi 


m 


1 

1 




T ■ 


^^^1 


HH 


» 














1 


Nov. 1906. Qrunwich Obun-ations of Comtl a 

1 


1906. 


95 

1 


J 


ObaenxUions 0/ Chmet a 1906, from Photograph* taken icith tfie 
30-indi liejlector 0/ the 7%ompton E^fuaiorial. 


J 


\ 


{Communimitd by th« Atlr<mom«r Bayat.) 




1 


^M 


The fuUowJii^ positimiij of Comet a 1906 were obtained from 
photograplis tftkeu with tlm 30-itich rvfleclor, with expusures uf 
froiu 3 minutes on January 30 to 20 minutes on April 14. 

The platua were measured in the aiitfo seraphic iiiicro meter, and 
the iHisitiou of the comet is deiiuced i<c*ym the mtans of aix 
reference ntura whose places woro derived from tbc catalogues of 
the Astnmomische GeHellschaft except on Febmarj' 20, when Green- 
wiub Obiervatious for the cataloj^'ue for 1900*0 were used. J 


1 


UftWandO.M.T. 


Aiiparent R.A. 


Appumit Dticl. 




Sort, tor PAnllax. 


^ 


B^A 


Dec). 


1 190^- 












^H 


' d 


ll ID 1 


h m ■ 


• J i' 




■ 


\ 


^^1 


Jan. 30 


'5 51 44 


16 16 It '57 


+ 53 33 «*3 


9-9992 


-0-52 


+ 17 


^^B 


Feb, 5 


9 34 14 


16 4 2717 


64 26 20-7 


99738 


-0-55 


•»-7-3 


H 


7 


12 21 16 


15 55 42-81 


63 44 52*1 


9-9688 


-1-08 


+ 3-3 


H 


7 


12 33 59 


'5 55 39-8S 


68 45 55 -9 


9-9688 


-1-08 


+ 30 


H 


13 


8 54 4] 


»5 5 55-23 


78 39 7*4 


9-9658 


-1-52 


-^5'3 


H 


30 


11 59 4 


7 22 4-42 


81 18 iS-6 


9-9912 


+ 1-57 


-3'2 


H 


»3 


9 53 »3 


6 27 3S'i7 


76 25 «7"l 


0-0087 


+ 0-63 


i-2 


H 


Mar. 2 


II 42 46 


5 SO 22-43 


65 15 234 


0-0589 


+ 0-71 


+ 09 


H 


3 


11 54 SI 


5 48 ZO-2() 


63 50 44 


0-0669 


+ 0-6S 


+ i'3 


H 


3 


*3 5 54 


5 48 1932 


63 50 6-s 


0*0669 


+0-69 


+ 15 


H 


S 


ro 26 39 


5 45 21 '95 


61 t6 i6'6 


OO82S 


+ 0-50 


)o-3 


H 


1' 5 


to 47 26 


5 45 30 '91 


61 15 10-5 


0-0828 


4 0*54 


+ 0-6 


H 


6 


9 22 21 


S 44 1601 


60 3 59S 


0*0909 


+ 037 


-0-3 


H 


k ^ 


9 34 49 


5 44 15*3' 


60 3 ZIO 


00909 


+ a'39 


-O'l 


H 


^k 22 


II 33 'o 


5 41 35 36 


45 3 577 


02135 


+ 0-32 


+ 2*9 


H 


1 '' 


8 6 18 


5 43 Si'4S 


41 26 8*2 


0-2567 


to-lK 


+ 1-3 


H 


1 ^ 


8 23 38 


S 44 1954 


40 52 35-6 


0*2634 


+ 0*19 


+ '•5 


H 


■ ^ 


843 4 


5 44 aa'\'. 


40 52 10 » 


0-2634 


+ 0-21 


+ i« 


H 


~ Apr. 14 
•9 


833 


'■i 3»"5 


f 33 59 21 I 


03602 


+ 0-17 


^1-9 

1 


1 

















~~^^ 


'" 


1 


96 Grecnwic/i Obxii/atuma 0/ Comet b 1906. 


Lxva 1, 


p 


Obttervatinns of 


^OBW^ b igo6, r*v»» PhotoyranftJf 


inltffn 


icith tht 


L 


, ^Chinch HejUetor 0/ Hie Tfi'im}ifion hU^uai 


iriaf. 




■ 


1 {Gt 


mmxtnieattd fry fA< Aitronvrntr lU/^nl,) 


1 


■ 


The following 


l>04itionR of Comet b 1^6 were 


obtained fraa 1 


w^ 


ItltoUigraphs t&kf 


n with tho 


3o-inch reflector, with exposuree ol | 




from 5 iiiinutea to jo tiiinutes. 










1 


Tbe plates were uioaaurod 


n tho uxtrou 


rauhic inieromotcr. 1 


■ 


Tbe position nf the comet ia rRferrod to ihe mean 


of 91 X 


"eferenw 


■ 


utarti whose |>lacej 


wero derived froai the cataloifues 


of the 


AstToao- 


1 


luiscbe Gesellschaft. 










1 










CoiT. lor P«r»Uu. 


L 


Dttke mhI O.M.T. 


A|ipar«ut R.A. 


App«rcut VWi. 


iMf A. 


K..A. 


Dtd. 


H 


^^^P d It ni ■ 


li ni • 


m 1 't 




■ 


n 


B 


H«r. 6 10 26 11 


II 34 43 86 


+ 1 43 34a 


9-6760 


-o'43 


+ 141 


L 


1 6 10 39 49 


:i 34 43'6o 


t 1 43 34*9 


9-6760 


-0-39 


+ 14* 


■ 


1 7 11 46 41 


II 34 i6'6o 


M 45 51 


9*6850 


-0-16 


+ 13-8 


■ 


1 7 " 56 I 


11 34 16-32 


+ ' 45 S'4 


9-6850 


-013 


+ I3* 


^ 


' 22 13 30 1 


M 27 51-4) 


-2 7 36-4 


"•3777 


+ 0*04 


+ a-l^J 




29 n 2 13 


It 25 13-63 


^ 2 16 477 


03861 


0x0 


'*' ' "^1 




Apr. 3 10 30 31 


1 1 23 35-88 


+ 3 22 io'9 


0-3935 


-o-oi 


+ *1^| 




3 W 44 27 


> » 23 35 70 


■r2 2a 107 


0-3935 


QtXt 


+ '"^l 




4 10 tS 46 


II 23 18-33 


■ra 23 6-0 


0-3951 


-otn 


-f '"^l 




4 to 39 25 


II 23 18-17 


+ 2 23 6'5 


03951 


o-oo 


+ s*^! 




9 10 15 22 


II 21 5965 


-*■» 26 518 


0-4035 


0-00 


-f *^^k 




9 10 25 21 


II 21 59*48 


+ 2 26 53*6 


04035 


+o*oi 


+ a-^l 




10 9 5 '3 


J I ai 4670 


+ 2 27 22-S 


04053 


-otH 


-f- 2'^| 




14 10 5 ]0 


ti ao S9'65 


f 2 29 2'4 


0-4128 


+-0'0I 


4- 3^H 




19 10 X [9 


11 20 1944 


f 2 29 29*1 


0-4339 


+o*oa 


+ **^| 




20 9 4tt 56 


i\ 30 13-93 


+ 2 29 21 'O 


4250 


+ 0-0I 


'*' '^l 




35 9 53 27 


11 ty 5915 


+ 2 27 39-9 


04356 


+0-03 


■*- s'^l 




36 9 sa 27 


M 19 5879 


+a a6 53*1 


04378 


+0-03 


4- 3-,^H 




a? 9 47 3 


It 19 59 34 


+ 2 26 ia"3 


0-4401 


fOo3 


+ '>*'^| 




28 10 ij 16 


H W o'87 


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tU the Liverpool Observalory. 



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Nov. 1906. Rev. A. JTenderson, Auroree observed in Ddting. 105 



Aurorm obierved in the Pariah of Deltiruf, Shetland, /torn Sep 
teinlter 1905 ta Hepietuher 1906. By the Uev. Alex. C. 
Hetitltirson, B.I>. 

1905. 

Sept. 3. No UD1181111I fenturi^a uoted. 

„ 32. VIsibL* from 8.^0 |i.iii. till 9,25 p.m. 

„ 25. Bi'giriiing a!ioiit 7.50 ji.m. 

^ 36. No uiHiBual featurvri uott-il. 

Oct. 7. A curtain iiunira, S.50 p.Tn. 

„ 2S. A*iriiriil li;:hl "tiiniiji: thi'i>U]|;h clouds. 

„ 29. Auroial li^iht iigiiin, tlimagh rloaJg. 

•Nov. 15, Cnniiioii, wjllj ;,'rei-u etrtt-iniem. 

„ 23. Nu unusual featuri'S noted. 



Dec 



29. 
30- 



1906. 

Feb. 15. A broad, white arch, 

„ 16. Xo unusual reatiirti» noted. 

„ 22. Kxti?!Tiiiiii^r iivcr liulf of tliv shy. 

„ 24. Qreoiii^h-wliitu. 

„ 25. OrL-eniph-wliita. 

„ 36. No unusual features noted. 

Mar. 13. 

It ' ?■ <t 11 

„ 24. At 9 p.ni. 

,, 36. A l>ri;!lit, I>ut ilUilcfinHd arch. 
A(>r. 10. A hroail :iri-.ti, willi HtrfHttiu'rci. 
., 38. A t>eautiful dispjar, chiefly lietweon to and 11 p.nt. 
Uert* fultuwa a ^iip, t-aused hy the absence uf night 
in tins hiltt-ixiL-. 
Aug. 14. Anrora, nrid «imiilianemis Bhowpr of Perseid meteorK, 
from 10 p.m. till 1 u.m. on 15th. 
., 15. Diffu-iid iiurorB behind cluud. 
Sept IS- Between 10 and 11 p.ra. 
M 16. 9 p.m., the KtrfiiiDi-nt nhoottng up from horizon 
through Uma Mujjr, and afterw.irdit forming 
ati an-'li. 
17. Reporled ti> me an hpin;; crimaoii and yolluv. I did 

not oliMtrvL* this ntinirM. 
33. Begun in tlie NNK ut 8.30 p.ni. (first ytilotr, after 
wards lijjht ffreen). At 9.30 p.m., fliKkerioR 
cIouiJs exiciidtid acroas the xenilli, aod tlierp 
Were cmcklin^ noises. 
33. Graenish-white. 

llfMMor Deltins, from which these auroras wereolwerved, ia 
in lut. 60* 34' j K ; loii^- 1* 19'! ^V'; loiiptudeiu time, 5 uiin. iSser. 

* At 7.40 p-in. tht TitDfon aurora extended in a brnad band mixh* Allair, 
n tlie iMutli nf il, Al 9.42 |i.m. tbv rii»giiift<.-«-nt green iilrcMmiin> 



MONTHLY NOTICES 



OF TllK 



ROYAL ASTRONOMICAL SOCIETY. 



Vol. LXVn. Dkcembkr 14, 1906. 



No. 2 



I 



W. H. Maw, Esq., Prbsidbnt, in the Chair. 

Major Alexander Davidecn Fleminij, Artiiletj ManeiooB, 75 
Victoria Street, London, .S.W., 

was balloted for and duly elected a Fellow of the Society. 

The following candidates were propoeed for election as Tellowa 
of the Society, the names of the proposers from personal knowledge 
being appended : — 

Edgar T. Adania. 5 Warkworth Street, Cambridge (propoaed 

by E. T. Whiltaker) ; 
Koberl Jonckhocre, Obwervatoire Stella, Roubaix, France 

(proposed by Ciunilie Klamiuarion); 
John Stewart, Chief Officer, U.1M.S "Emprow of China." 

The Willows, Wallasey, Birkenhead (proposed by E. B. 

Knobel) ; and 
Samuel VeevetF, Normanton, Kimberley DriTc. Great Crosby, 

near Liverpool (proi^wpd by IL C. Jolinson). 



Seventy -seven presents were announced as lavinc been 
^teceived since the last meetinj;, including, amongst others : — 

W. Bramsen, Japanese Chronological Tables, presented by 
. B. Knobel ; i )pucai (,'onvention, Proceedings of the Meeting 
!av-Juno, 1905, preaented by the Committee; Oxford Astro- 
-ralitgiiH, voL i., piesentud by the University Observatory, 
V. pHfkhurst, Reiiearcbefi in Stellar Photometry, pre- 
'othor ; Royal Observatory, Greenwich, Astronomical 
presvnled by the ObpervaUiry ; Royal Ohserva- 
Hope, Annals, vols, x., xii., Aatrographic 
by the Observatory, 



loS 



Pi-cf. B. H. ^Mnwr, On the Possibility of LXVa % 



Aatrographic Chart : 20 charts, presented by tlie Royal Obsem- 
tory, Greenwich, and ig charts presented by the San FerDando 
ObeOTvatory. Photographs of the jupectrum of Mira Ceti, pw- 
Bented by the Rev. W. SiJgreaves. 



On the Poteitniitt/ of Improving the Plcufv of the Reference Utan 
for tiie Aetrograpkic Catatogue frmn the Photot/rapiiK 
MfimtrM. By H. H. Turner, D.Sa, F.R,S., SavUiio 
Profeasor. 

I. On each of the plates taken for the Astrographic CfttalogM 
there are certain stars of which meridian obiwrvations have been 
made, and the couBtants of the plate arc found by using thne 
recorded places. But the pitu-es are often defective, frcim entm 
of abwrTation and accumolated proper motions ; and the emcs 
are indicated by the realduals fuuud ou comparing the pbotograpluc 
measures (reduced with the plate-eonatanta fcmnd by using all Uu 
stars) with the individual meridian places. But these residnali 
cannot be taken as sattsfactory corrections to the adopted placo, 
because the plat^-conatants, having been found from faul^ 
meridian places, are themselves faulty. 



N 



+ 3 

I 2 



W 



S 
Fid. I. 

2. Taking only a Hingle i)late, if we correct the adopted {dacM 
by the residuals found, and then solve fur plate-constants agam. m 
shall get t^rccEsely th<^ same constants as before, and the rvsiduab 
now will be all zero; but the Iniprtivoinent is of conrva only 
fictitious, and no real advance )im li^en made. We need nolt 
however, restrict ourselveo tu 11 Htngle plate. Krery &tar occttn 
on at least two plrites, and we got iit Ji-asl two different t-esidnab 
for it, Moreover^ the siara In tlio fimr <|narterB of any pUtc will. 
as a rule, be on four diffurunt (i*- 
adopt as corrections to the 11 
residuals for each ntar (tmimlly tv,.- 
determine the plate cnnatanta iif> 



objection to thia coiirne ; but it 
best possible, for the following r< 

3. Callthoresidutilsdfli'i 
from other plates H: it in 
portion |A is simply noa-alt* 



plates. Sball we lh< 
.(i;efi the nieana of 
uinotimee more), and; 
in no printa 
jhethor U {g' 



■Ul tlwni 



Dec 1906. Imprm^ng the Place* of Reference Stars. 109 



that if the reaiduaU A be appliMl to the orij^iQal places, aad the 
ooiistaiit-s redett^rmineil, they will be the fiame as before ; in other 
words, if we determine tbe eorreetiorui to n, 6, c by solving a seriea 
of equations such as 

Aa. j: + At.y + Ac = a 

we shall get Aa — o, A6 = o, Ac=o. Naturally wo ahall got tho 
name zero rentalt if we write ^A instead of A on the right of all 
the equations. Hence it may bo argued that we may aa well Kave 
ourselves the trouble of introducing the system of resiiluBls A into 
tbe equatiuna at all, since they do neither good nor hurm; with 
one pomilile qualification. Some star? occur on more than two 
plates, and if we form tho mean of aU platca, the residuals A will 
have a factor ^ or ^ in some cases iustcad of |. But there is 

trlj no systemHlic advnntage to be gained by such exceptions, 

I we need not discuns them in detail. 

4. The question therefore ariaea whether tt is not better to 
exclude the reaiduala A altogether, since Umy d» neither good nor 

' harm In improving' the plate-couatonts. Should not the coricctiuns 
to the originally adopted places be determined from residuals- B 
entirely 1 — i.e. instead of neglecting the ^ A aa useless, and retaining; 
the ^B, should we not substitute B simpiy t or the mean of several 
B roiiiduals if they are available ? TLie answer to this question 
can only be arrived at by considering in some detail what the 
tesidualfi represent. 

5. For each star we write down two equations of the form 

ox + ^y +c - X = o, dz + ey +f - y = o 

rand it will be suffiuleut to consider tho Brst of llese equations 
only, since the pruceduro is tho same for both. In this equation 
X and 1/ are the co-ordinaten of the star, a, b, f the plate-ronstants 
to be determined, X the difference between tbe measured and 
calculated siiandanl co-ordiuates of the star. There will be ae 
many equations as there aro known stars on the plate, and they 
may he solveil hy lea.?t ttquarea or any equivalent process. At 
Greenwich and Oxford the labour of least squarea has beeu avoided 

'by taking the mean of all thu equations for the S and N halves of 
the plate and for tbe E and W halves ; i.e. the four equations 



/(n4 + n;)=.o 



KaTO been formeil : where [[] npr«seDta the sum of all the 
easious 

OB+fiy + c-X 




* of the plate marked i in fig. t : and »] is the 
portion. Next, the constant c is eliminated 



no Ptof. H. H. Turner, On the PimihUity of 



by subtr&cting the second equation from the &r8t and the fo 
from the third, and we get the pair 






from wliicb to determine a and b. 

6. If the staK ure equally distributed in the four quadrants, 
that 7ij <= ri^ = n, = f)f , these eciuatjonv reduce to 

[i] = [3l and [2]-[4] 

The discussion thue divides it^tf into two p^rts : Grst, the coustd 
ation uf what happens when the stars are nniformly distribatcdj 
a.nd secondly, the effect of trre;.'ular diatiibution. 

7. We shall take uniform distribution first ; and we mny 
the very simpleflt case of it, viz. when there are just four at 
placed at the centres of the four qitadrantK. If the side af tbi 
plate be 4«>, the co-ordinates of these sX&i% referred to the centre of 
the plate as origin will be (see fig. i) 



I 


a:— -*t 


y=-« 


3 


X= +if 


y= -« 


3 


x= +* 


y= +« 


4 


:C=> -« 


y— +* 



and the equatiou$ for finding a and b become 

+ 3g.a — 2a6 = Xg - Xj 

Thus 4*-« = - X| + X.^ + X- - X . 

4,.i.-X,-X, + X,+ X, 



and for c we add all four eiiuatiouB, ao that 

4C=X, + X3 + X3 + X,. . . . (3) 

8. The residual Xj is reduced, with tbt-se Taluos uf a, b^ and e, 10 

which on putting x= -a, ,(/•=-«, and the values of a, 6, c gifen 
above becomoft 

l(Xj-X, + X,-X,)=+I,aay . . . ^^) 

9. The residual for the third quadrant ui also reduced to + 1 




Dec 1906. Ivijii'&oing the Places of Referente Stars. 1 1 1 

t while the residuals for the wcomi and fourth qnadrAnta become 
— I. This quantity I, therefore, cannot he removed by a linear 
•ohition. 
Its effect is to alter the square F (fig. 2) into the tntfiezium Q ; 
and it may he produced, not by erroiieoua adopted pUc&s hut by 
a "tilt" of the piato; or, in other words, by our assumiug the 
wrong plate-centre to which to refer our standard co-ordinates. 
It in known that this modifit^s {, ^ into expreseions of the form 






bti+e 



. { 1 + a')i + br) +e' + k^ + i^ approx. 

where {k, I) are the co-ortlinateB of the true centre. The terms 
which give rise to an I effect are the fij terms, which are positive in 
the first and third quadnints and amative in the second and fourth. 
But it is known from cxpeticuce of plates, in parts of the sky 
where stars are numerous, that no very large part of I is due to 
tilt in this way. 

ro. It is perhajw also tm well to Terlfy that th« same I term 
would be given by the muthoj of least squares, at any rate in the 
laimple case at present under coasiderutiou. Solving (be equations 

— Off - As + c = X, 
+os-6»+c— X^ 
+a«-^6«^+r = X3 

by least squares, the normal eqoations am 

4*^a = *(-X, + X., + X,-X,) 
4^/,-s(-X,-X3-fX,-KX,) 
4^ = ( X, + X3+X, + X,) 

which are precisely the same as those obtained in § 7. Hence the 
const^tnts and residuals obtained are the same, and we still get the 
lesidiials +1, - 1, + I, - I for the four quadrant* where 

4l-=Xi-X,-KX3-X, 

It. It is convenient to h^ve a name for the quantity I, and the 
name "inconsistency" will be adopted in the present paper for 
convenience. When I is not zero, no linear solution will fit the 
plate. We can fiiid the value of I before applying any linear 
sotulion at all, since it is not altered by the application of linear 
terms. 

12. Now it is clear *hat the procodnra indicated in ^ 2 and 3, 

•■■intf the means between residuals from dilTerent platen, will 

the "'inconsistency" for any plate ta zero, 

even this is not certain. Calling the 

L. and of the fonr overlabDinB nU^«& 




12 



Prof. H. K. Turrur, On Ou Pombility of LXVR 



+ 1], -I5, +l8, -I^i then the process of ta)(ing the neao 

residuals suhstitutari for ]p the quantity 

The firttt term represents a certain gain, since 1^ is halved ; 
the second term may either increase or diminish thtt first numerical! 
Oq the average we shdll pcrhnps not Advance boyond halving 
original inconsistencies. We con, of course, proceed to a mo 
approzimatioii and halve them af^ain ; Hud to a third. And 
uaing the invariant property of the inconsistency we cau 
these approximations without performing the solutions 00 
plates if we xiinply have tite inconsistencies fur all the pi 
tabtiliitod before us. It is even easy tu »umnittriso tliiit pre 
approxi million alj-aliraically and combine several steps ii 
But, probably it will be better in practice to watch the pi 
numerically. Thi< etui tn h^ attained is the reduction of 
ioconsistencies to small quuutitiei}, zero for choico. And tk 
question is suggested, Ts there any siinijlu process for making tfaui 
a]l 7.ero e» blocl If we knew the correct place)=i of the stars aod 
had perfect phobo^^rnphia meosuitis, the inconsistencies would be ill 
zero. The measures are not perfect, but the errors of meaanrencot 
may be assumed HintUl cunipattHi with the quantities ^iven below; 
and the problem is to find a sei uf pluccs fur the Ptandard stan Id 
tit them as clost-Iy i\s possible. 

1 3. We may still Mippose the standard stars to be arranged 
exact rows and column^ four on each plale, and each one conimeir 
to two plates. Let us ruj)rt'sent a set of advaiUageooa carrect)OBi_ 
to the adopted places of these starH by the subjoined schetue :— 

o, 03 a, a, . . . . 



*, 


1^ 


''.. 


64 


. . . . 


'H 


Ic, 


«a 


'^4 


. . . . 


<*. 


•^j 


•^8 


d* 


. . . . 



SO that the four stars on one particular plate, for instance, ivqinn 
the currections b.,, 63, q, c^ Then if wc reduce the inconsistency d 
every plate to zero we have a seiriM of eijimtions of the form 



- 6j - Cj + Aj + Cj = 4 [ BaC,] 



(5J 



where the symbol [B^CJ is_, 

14. Let R lie the 
equations. There 
altogether 4 n star 
plates, there will be,| 
n equations among 2 
ways of salisfyiag them 
plate we get n 
determinate. 



mt the inconsistency. 
ami therefore of 
loi each pkte, and U» 
eh star occurs on 
•er. Hence we 
TB any numh 
'm[>tmu for 
flit 



Dec. 1906. Improving the Places of Jieference Stars. 1 1 3 



15. Suppose we make the assuniption 

ftj + Cj+ij + Cj^o . 



. (6) 



I tlial 16, that tbe mean cotrectioD to the places on auy plate is zero, 
or the plate-cotiBtant in uQdUlurbeH. Tuia aeeiui a natural aasiuap- 
tion to try, at any rate in thu firtiC instance. Theti, combining the 
two equations ($) and (6) (or the same plate, we get 



&,+ «,= -2[B,CJ (ia + <^="<»Al 



(7) 



4,^0 



We can cover the 
an 1.1 so on, 



*that ig, the inconAJstency is divided equally Wtweeo pairs of opposite 
quadrants . 

16. Now if we follow the diagonal line of stars a, h,^ Cg d^ we 
\ have a series of equations giving a, + 65, b^ + Cj, Cj + d^, and so on. 

Hence if w« know any one correction u^, we find siiccetisively fcj Cj 
d^ and all the rest. 

17. 11 is to be noted that the case is not the same for the 
adjacent diagonal ia the Dame aeusu &. r^ (/, . . . . and a^h^e^ , . . . 
There aie, according tu the echeine au''»pfced for the Astroii-raphic 
Catalogue, no plates running with corners in this direction — no 

[plate c^Cjd^d„ for instance. In covering the sky twice over, we 
select two only out of four poasible ways of covering it; for con- 
sidering any single plate 6^ c„ Cg b^ l«t us characterise it by the 
star at thfi left-hand tup ronieT, in this case fcg. 
sky completely by plates 63, 6,, 6j, . . . . d*, d 
without using systiMiis in which b^c.^r^ u.U' represented at all. 
And by the achemo adoptt-il fii'r the Aslcographic Catalogue, tbu 
overlapping plat&s would be the system c^ including plates c, e^c^ 
• ••■><']. *»i *6 ■• - ■ ^^'it not iucludiiiK c^ (ir b^. The systems A, 
and c^ would overlap the others in a different way. Had these 
additional ]>lates been taken, we should have had 3 n equatious for 
inconsistency of type (5) instead of n only; nud we could have 
determined the corrwtions to the star plnce» completely from these 
alone, without any additional a.-<su captions. 

18. The absence of the plates of type 6, and e.j prevents the 
formation of equations for 6, + Cj, c., + d^, etc., but we get h^ and r^ 
from the dii^^iials of the other sense, a., h^ and n^ b^ c^ d^, and 
so on. Hence if we know or lusunii' all the a% we am find 
all the other t<trms. Or aimilarly if wf know or aasume a, t, c^ d^ 
.... we c<]uld follow liie diagonals from these aa startiag- points 
aud fiud all lht> qiiantitiea. 

19. But it will throw light on the validity of the assumption of 
aquations (6) if Wf take an actual example. We have hitherto 
been assuming nn ideal distribution of stars, one and one only at 
the cvnlre of each ijuadrant. In passing tx) an actual example, we 
■uusl replace each ideal star by a number of actual stars scattered 

•he quadrant, aud for a single residual we substitute the 
■everal, 

»ie changes will be understood without further ez- 
followinft BzamDle clodelv repieaents on actual 




1 14 Prof. H. H. Turner, On the Possibility of 



inateaee vhicb occurred in the usual courw of reduction uf 
taken at Oxford in rone + 39', at R.A. 4** 7'", where the stara 
few in uumljer. The original solution for plate-con a tauts gal 
resiilQaU far sumQ slarii differing by quantitinn etich as 0'oo6b l' 
and 0-009= 2"-7 from the residuals fuund from adjacent pli 
A new solution for plute-oonHtatitA was acrorclingly made bv li 
squaree without removing these anomaliea ; and vurious assoi 
tions as to error In scale valne. etc. were tried without succwa. 
21. In the light of the conaidorationit above advanced, tbe 
consiftenciee of this plate nod of overlappio^ plates were calcuh 
with the following approxinmto ri'sulte (the precise definition 



4" 3' 



4_h|2r 



+30' 



42fl- 



+ 3 0^ -30 



-3 



-19 



+ 13 -IS 



_-£^Q.2l 



-Z t 



♦ i-a 



^"3" 



4-iZ' 



♦ JO* 



» za* 



N 



inconsisteucY for stars <.-iisimlly dintHbutcd has not yet beeu 
and henKc the resulta are provisional only) : — 

Zone+30', Kor U-A. 4'' 3*" 1= -30. Kor R A. 4^ la" I 

ZODe+29', For R.A. 4'' 7'", r= - a-6 

Zone + 28', ForR.A. 4" 3" 1= + 1-9, For R.A. 4'* la-" 1=. ^-i^J 

Tho unit for 1 Js o'*3 or '001 of a reaeau interval. It will 'bi 
seen that the platee nverlup by 4*"'" in one direction and 5'»» b 
the other, anil are thui' not Htrictly diviiled into finarttrs ; hut 1st 
ns ni^lect this for the present. Tlie values for I indicate that tbt 
mean residuals (observed — adopted) in the quadrants are dispoH^ 
as in fig. 3. 

33. In tbe quadrant AC the agreement of Uid two plat - 
hut in none of the other quadrants is it at all sat 
linear solution can Improve it, for such Holutinns o 
and it will at once bi* undersUKnl v.-'w ' ' *iv ti 
altering the scale value by some a 

23, We must begin by a*f!nming a. 
outside quadrants. In default of > > 



>ec. 1 906. Improving ike Places of Refertncc Stars. 1 1 5 



[i]Iuatr>itioo merely, let us as'tume zero corrections for the top row 
)f quftdraiiM FA, AG, GB, anrf BJl, 

Then the correction to AC lumt be + 6-o, in order U> take up 
Itlie +3'o lUiJ +3'o in the two quadmnts FA, AC. 

The correction to CD will be 



ud to DN 



* 2-6 + 2-6-6'o- -o'8 
-rS- I -8 + 0-8= -2-8 



[8imilHrIy following tbe diagonal HL we got corrections to 

RIi = o 

1JC= ■}- 2'i + a'l +0 = +4"2 
CE= - 3 "6 - 2 "6 - 4*2= -9'4 
EL- + i'g + i'9 + 9-4= + 132 

The incre&se in this lost set is alarming, and suggei^ts a reviiiion 
of the original asfliiraptions ; hut we will first finish the example. 
The central plate is miw Im be reviaed an follows : — 

We correct the udopicd places of the stare in the four quadrants 
by the fgllowing quantities 



+ 6-0 
-9'4 



+ 4-2 

-o-S 



I 



aud then solve the eqiiatiunu for Hcule values and orientation again. 
The eflecta on the couvtautti a and b arc shown lu equations (1) 
and (3) of § 7 ; that on c was arranged to be zero. But what 
immediately concemA us is tbnt whi>n this now linear solution is 
applied, the mean residuals in the four quadrants will now be zero; 
for we saw in g 7 that the effect of the corre<;timi« above tabulated, 
taken by themselves, is to leare us with four numerically equal 
residuals of the value 

± 1( - 9'4 + 4'» - 6'0 + 0*8) - ± 3*6 

4nd those will just iieutrvlise the residuals ahowu by the original 
BolutioD. Indee<l, it it* the basifi of the method to reduce these 
resiflualji to wtro. The same will be tme of other plates, and 
hence tlie diacrepaucics between adjacent plates will disappear. 

24. This will only be truu in tb>< mean, i.e. at the ceatre of each 
quadrant. For stars away from these points errors in a and b 
will etill intMiliice diacrepani'ie.^, hut they will be naturally 
smaller. One thing at lenst is clear : in default of some systeni of 
fnn-priinn of tlie kiod above indicated, there are bound to be 
> i«s between ailjacent plates in thinly starre^l regions, due 
r of measurement n»r rediiction, which cannot 
T change of the linear wiliition based on the 
places. To get itiiprov»^nient we must alter 
^ one another ; and ut tinit Hi^^ht this aeema 
't moffi dnwtic than any other modifi- 
-— takmg the mean of the residuals 




1 16 Prof. H, H. Turner, On. tlie PosttbUity of nva 

25. As reganlu this latter process, we may note in passmg 
ineffective it may be in helping us to remove discrepttncies 
plates. lUcurriiig to {ig. 3 (p. 114) we see that th« cat 
suggt-iitud by taking the meantt from adjacent platuu are aa bel«* 
those 8ugi;est«d by observing the hicuiisistency being put aloi 
for comparison : 

By " mMiia "' By " lnconilrt«ncT " 

+ 3"8 - o'3 +6"o +4'2 

-o'3 +0-4 -9'4 -0-8 

The set obtained by ''means" would leave ns, after a 
solution, with residiiBts of Tinmerina] value 

± J( - 0*3 - 0-3 - a-8 - 04) = ± 09 

for thii) plate, which is certainly Len« than the ± 2*6 we 
with; but to get rid of the discrepancies altogether we apj 
require quite a different set of wr ructions. 

26. We return now t^j the assumptions made in deriviDg 
com^ctionn, which can obvicuHly be improved. Let us firet 
aider the effect of a different set of starting-points in the top 
of quadrants. The iliagonal H B C F L, for iusUiuce, gives nit 
series 

which '\f> becoming alarmingly large. How mncb of the increoM 
due to the assumption of zero as a star ting- point ? It u 
seen that if wo start with +0, the effticLH on the aeriea will 

+ a, -a, + (1, - « 

and thua if we pat a = + 6'6 wn get the seriCiS 

+ 6'6, -r4, -2*8, +6*6 

Thus, if the sum of one set of altenmt^^ tcrnis in a diagonal diffen 
from that of tho otiter set, we can reduce the difl'ereiice to zero. 

27. Consider next the other set of a&iuniptionB represented by 
the equation (6) of |; 15, 

&2+e, + A| + ea = o 
If we make the altornativo nesumption 

6j + o, + &,+c,-4^'. 
tbeo combining with the equation for inconuisteDcy 

we gt>t 

A, + c,= 2[[UXJ + *| 

If we have started liy aMunii'i-? f 
A's; and equations (9) and 




1906. Im^iroving the Places ctf'Be/erence Stars. 



"7 



lint all the otlier correctionn in two diagoiuUti will be moditieil Tiy 
[the quantity /*, with alternately positive and iiegativft signs. Thus 
tif tlie two diugonala originally read 



00 



O'O 



+ 132 



+ 6-0 
-94 



-08 



-z-8 



pwe can add the (tame quantity, say + 5'i, to both - 9*4 and — 0*8 
iproTide<l we AubLmct it from +133 and -3*8, and add it to tho 
terms next to these, and so on. The fev terms giveu abave will 
[then read 



00 



o-o 



+ 8-1 



+ 6-0 
-4'3 



+ 4'2 
+ 43 



-79 



28. It is clear that we have ample racilitiuii for devising sete of 
; correctians to the originul places which shall make overlap|)ing 

plat«a accnrdaiit ; th^e qui'stion now fieomo to be how to limit our 
choice. It seeraa probable that in practice the limitations will 
arise from the necesMity of satisfying known conditions foi* 
particular stars. Huniiiu;; down a diagonal in tlic manner 
indicatefl, we shall cvonie to stars with well-determined placet* 
aoH known proper motiona, and the pmpor correction to the 
adopted ptiice will be known within narrow limits. Such a 
inotlii»l canniit bo- disiMissrd in grnt^ral tcrmti, hitt will he ripixial io 
each particular case ; though cvperience of seveml coses may 
8U4;^eHt siome general rcinarkii. Bui it seemi; dear jthat it will serve 
a useful purpose to caltiulate the '* inconeistency " of every plate, to 
exhibit the resultii in diagrammatic form, and then fornnilate an 
empirical sot of corrections. This work has becu put in hand at 
Oxford, but will naturally take a little time to complete. 

29. Moanwhile, it iSL-ema desirable to pnblifth this note for the 
fcdhiwin;? rea.'ion. We have formed at Oxford lerlgers of the 
corrections to the standanl stara from all the plates on which they 

.occur, and have June much work in examintug the larger dia- 
'^crepancie*. In many eaava, of course, they have been traced to 
nitre numerical errors ^compiirativety seldloni to orroi-s in measure- 
ment), but a sensiblo number have [lersistently defietl explnnation, 
and yet are ao lar^ie as to suggest an error. It is now rerdlHed that 
these are due to " incunsistvncy " of the plate as above, and that the 
time spent in looking for errors or lor better plate-cou-staots was 
'ime last. Before contlntiin^' the examination of large 
, we propose now to tabulate the inconsistency for each 
ow many diiH^urdances can be removed hj suitable 
"■ms po^tiihle tbut u note of warning may save 
•ho may have encounterdd aiicilar pnz2ling 
>rhaps a fair excuse for publishing an 




Il8 



Tmpromng the Places of Reference Stars, umi. 



30. [Paragraphs 30 to end added Deoamber 3.^ The *\ 
psivgraphs (except ti and 13 which bave h«en eocpanded) 1 
circulated in prouf to several autronomem, and various critici! 
received. Krom Bome of these I recognise that undue jtromiDc 
hflB been giren to tlie methodit indicated in ^ 13 to 27. Ix 
not intended to represent tliem as satiafacton* (thin »houId 
clear from §^ 2S and 29) ; but in tliat case they might hate 
curtailed. 

31. Further, it is well renmrked hy Prufessor Dywm 
there mny be independent metlnvdB of iwprovinj^ the pi 
corstaiiLK, fi.g. vre may be able to a-nsume that a and c. 
coastants far scale value, are known from other plates ; whiU 
and d, the orioutation conKtant^, strengthen one another. 

33. But the nmiti point suggested for consideration is 
touched. To make thi! point clear, I venture to restate it 
follows, modifying the Btateinent «o as to take account of § 31. 

(a) Fitid by any mi-thutl the best linear solution for a plate- 
Denote the mean reaiduala in the four quarters by x^ x^ ^'|l 
an<l let 

41 = ^,-2^+3^-*, 

Then I wilt be the sani(> whatever linear solution in applia^ 
or before any is applied at all ; and if I is not zero, no 
solutiou will tit the adopted places. 

(/') If we re^^iird x, x^ x^ x^ as the pniper corroctions to 
adopted places of the at^rti, then after applying them the ni 
valne of T will be zero; and we have a set of adopted pi 
which can be fitted by a linear eolution, viz. the solutiou all 
found. 

(c) But we must take account of overlapping plates, and Umm 
du not indicate, in general, the sarao correclioas : they give, 1^. 
x\ , x'^ f ^j, , x\ , Shall we then adopt an corrections 

This procedure hos the obvious advantage that we have oalr 
one correction for each star instead of two discordant onee ; bnt it 
haa the serious disadvantage that the iuconsietency fur each platt 
is not made zero. 

Hence the corrections cannot be re^'ardefl a.<t final. When «• 
apply them to th*^ adopted places and make now soluliuna for cmI 
plate we ehnll havt^ the same situation as at 6rst : the residnati 
from overliipping plates f<^r the same star will not agree. 

(d) We can, of course, repeat the procesa: again Xmke 
of the residual)!, and afcain find new cor 
third approximation and a fourth ; and wi 
the process is not endleiwi. A ne(X»$ary co* 
last found satisfactory places is that the v 
should be zero, or at least so snifll' '^n' <• 
ways — tilt, defective measures. 




)ec. 1906. Poffsons Ohservaiitms of U Otminontm, 1 19 

tve no gaarantee that the inconsistencieB will be reduced bj this 

jethod : thfly may even he incrfca«ed. 

(e) We can only find by actual trial whether this is or is not 

le owe. When we havo tabulated the inconsiatencies, we can very 

lickly test the affect of tiikiug means of overlapping pliites withoul 
performing uny actual solutions. If the proccBS is conver^-ont, we 

in adojit the results to which it leads just as satinfactorily as we 

in take means between two plateti in the first instance : if the 
jroceas is not convergent, the first step id as wrong as any other ; 

id we detect places where new meridian observations are CmperaHm 
any aiivaace is to be made. Needless to remark, additional 

leridian ohservationfi will be always welcoiuo and helpful ; but 

ley may not be iinmediately forthcoming. 



Po'fgon's Obsfrrationt of U Geminorum. Edited by 
H. H. lunior, D.Sc, F.R.S., Savilian Professor. 

1, Id 1904 April Mr Joseph Hoxendell, of Southport, put into 
I the writer's hands a number of MSS., notebooks and charts, 

representing the work of his uncle, Mr N. R. Po^n, on Variable 
fitani. Mr Baxendell found that he had not the leisure necessary 
to arrange the nifltevial for publication, and expressed the hope 
that the editing of Knott's and Peek's observations (Memoirs 
R.A.S., vols. lii. and Iv.) might be extended to Pogson's. A pmall 
grant from the Governtnent Grant Fund enabled me to get the 

J original notebooka copied out, as a safeguard against loas or injury, 
and the charts were photographed by Mr lJi-!Uuiiy and thu originals 
deposited with the ttoynl .Astronomical .Society. Hut as yet I have 

imatle but littlL* headway with the actual cnpy for press. The 
inut^irial requires mom study than might be expected, some of it 

I being very scrappy. 

2. A recent announcement of a prize question on the variable 
' V Genvinnnim, by the University of Utrecht, produried some 
! inquiries for Pogson's original observations of this curious variable, 

and luriiwl my thnught-s in a now diroctiou. Instead of trj-iug to 
deal with the whole material at nnce, which wontd require at least 
Hveral weeka' continuous attention, could the observations of 
[individaal stars be published separately 1 As an experiment, the 
observations of U Gemioorum have been collected jis below, and 
their immediate publication will in any case serve the good purpose 
of putting this valuable early matctiiil in the haiLds of those now 
undertaking a discussion of this remarkable star. 

5. Pogaoa began to hiok for this storaoou after Hind's discovery 
'>^N i)ecember 15, anil his first observation of it was dated 
'^h 26, when he makes this note :■ — 

-•iable sabject to strange fluctuations at intervals of 

da, ai ■■< to the extent of 4 mags. The 

steady, not at all twitchiug like 



120 



Prof. H. ff. Turtur, Pogson's 



LX\U 



tbe variable. The phenomenon (which was quite new to 
was vratclied for above Imll-nrt-liour with povrera 54. 65, and 
At tinicn it quite vanishud, aod then surpassed tbe com[i 

star a. 

On the next night, 1855 March 27, he notes: 

Far from 8t*ady, hut the pulsationa much l*>«s marked li 
last night. 

And he seemp to have looked in vain for a repetition of the fli 
tiouB of hiii first obi^ervation. Thu^ he Dotes on — 

1857 April 15. A fine sky, but dermiliou rather nnnt 
U is certainly low( steady than the neighbouring stars of 
magoitodc, but not in the marked manner previously ol 

1859 Kebniary 16. No extraordinary appearance different 
neighbourin;^ start;, except that it was rather le^s sharply defined 
than they wure; the colour v/aa a leaden white, not at aJl red 

With these exceptions the notes made are not of ^^reat int 
Many of them are aimpiy "fire sky," or "moonlight," or "puuif 
clouda"; and it seams unnefre-isary to encumber the record 
ihem. Those likely to prove of value are here collected. 

1857 April 7. 1hn aouth 93 certainly bri^ht^r than the north. 

1857 April iS. In a apleudid aky, just suspected. 

1857 October 30. Well compared; certainly on the npid 
increase. 

i86'4 September 28. Star 124 very little letst than 113. 

1866 .April 16. Well aeon aud compared at 8 p.m. About 10) 
p.[u. decidedly bri(;bter< 

1868 November 17, iS, Either IT or star 142 of S^xeiid^ 
seen. 

1870 January 17. Bright yellow ; moon totally eclipsed. 

4. The teleacopes used by Mr Pogsou at various time« ud 
places were oa followa : — 

At tfiH Raddiffe Observatory, Oxford^ to end of 1858. 

E'luatorlsl at R«dc1iffB Oljservatorv. 
lUiDBdcD portable telMCOpa. 
Dolland portable te]onop<>. 
"Sttivthlsn" or " Lm": ao()ttir«d tram 

Adm. Smyth by Dr tea of Hart«4i, 

aind lent by him t/i U^ 

is 1857 (SiMcuInn 

Tak«n ImcIc to T 

Mr PopfD anv 

Ap|i«reij 

liini. 

Oct- ^ : 



pwtton. 


Apprtiiro 


Fociu 
In InebM. 


X 


72 


120 


s 


3-2 


30 


Dd 


3-8 


42 


SI. 


3-» 


60 



Dec 1906. Ohaervatwns 0/ U 6eminon(.m. 



12 E 



At t/ie Hariwell Ohtervatory^ 1859 Jan. 1 to xS6o De& 31. 

SL 3*8 60 As above. 

H 5*9 loz Hut«ri?|l Ei^tntorial. 

Da 8'S ... Mr Dawen' t'Vtiiatorial at H«dd«iiliain, 

B lov 144 Mr Barclay's Kqnatorial at LeytoQ. 

At Madras^ i36i Feb. 3 oawaroB. 

L 6*0 ... Li;rebonr« E<iuatariiU. 

D 3*5 ... DoUoad tele«Mi>e. 

8 8x> ... Sinms Equatorial. 

SL 3'8 6a Smytbian or Le«. 

5. Many of the oWrrationd of U (lemiuoruiu in the first ten 
jaara are recordB of invisibility, with eatimated superior limits; 
and to save upace^ theso ure coUucteJ in Table I. 



Taulb I. 
Datts in til* YeurM 1856-1865 when U Ofvtinonem wa* Icttldjirf 



l>Kte. 


Tal. Power. 


lalarrMl. 


nai^^. 


T«l, Power. 


laMmd 


1856. 
Jbb. 2 


E 


54 


<I2 


1856. 
Nov. 26 


E 93 


<'35 


a? 


B 40 

UaximutQ here. 


<JI 


Dec. 


29 

1 

IS 


it 

i> 

E 54 


<'3*5 
<'3*5 

<I2*0 


Apr. 2 


1 




*I3*S 




24 


R 40 


< iro 


4 


1 




<I3 




37 


K 54 


< ■a7 


10 


1 




< 12 




29 


E 93 


<'35 


16 

ao 

24 
Hay 10 


t 
T 
K 
E 




<rf-t-o-5 
<ii-o 
<#+ 10 


ISS7. 
Jan. 14 

>5 

16 


K 93 

E 63 


<i3^ 


13 

ao 


<i 




<d 




37 
29 






1 w 


■• 






Feb. 


3' 

13 






^K 






<ii-o 




14 






■ 


1 




< iro 




16 

2(3 
23 







122 



Frof. H. H. Turner, Pogsm't 



Table L — eotUinued. 



Lzmx 



Dftta. 


TaL Power. 


Intemd. 


DMe. 


Tel. Power. 


IiAnl 


1857. 






1858. 






Feb. 38 


E 65 




F«b. 


»9 


8L 50 


<"T 


M»r. 3 


II 


<d 




21 


>i 


<irt 


4 


E 95 


<f 




38 


I* 


<'n 


13 


II 


<13'0 


Uar. 


5 


ti 


<ii? 


13 


■I 


<i3"o 




8 


II 


<iH 


17 


II 


<»3*5 




9 


E 96 


<»31 


20 


•■ 


<I3*5 




11 
17 


SL so 
E 96 


<ij-S 




Mazininm hare. 






ai 


SL 50 


<II'0 


Apr. 18 


E 95 


<i3'S 




22 


B 54 


<iifl 


May 5 


E 6s 


<li-5 




26 


11 


<iii 


Aug. teS 


SL 90 


<ii-5 


Apr. 


I 


SL so 


<ia'o 


Sept 17 


1, 


<I2'0 




10 


E 65 


<i3< 


18 


II 


<I2-6 




13 


II 


<i3'o 


Oct. I 


SL 50 


<II'0 




IS 


■I 


<1I'0 


7 


It 


<II*0 




17 


II 


<II*0 


8 


11 


< 107 




33 


II 


>ii-S 


13 


,^ 


<I2'5 




30 


II 


. <»3'S 


16 


II 


<I2-4 


May 


3 


SL so 


<irS 


27 


It 


< I2'3 




6 

7 


E 65 
II 


<tiv 

<12'5 




Maximum hare. 






II 


It 


■<i3"o 


Not. 16 


SL so 


<I2-5 

<'3-5 
<i3'0 

<'3-5 




19 


B 41 


<:in 


18 

28 

Dec, 19 


E 95 
E 54 


Sept 
Oct. 
Nov. 


12 
8 

2 


SL 50 
E 6s 
H so 


<I2S 

<i3*i 


1858. 






9 


SL 74 


<:i3S 


Jan. 9 


SL 50 


<I2 3 




Maumam here. 




1 1 






<I2-5 










13 






<i2-5 


Dec. 


2 


SL 100 


<I2S 


18 






< I2'5 




26 


SL 50 


■<iro 


20 






<I2'5 


1859. 






21 
23 






<I2-5 
< 121 


Jnn. 


5 


H 50 


-ein 


25 






<ii-5 




7 

12 


II 


-CIJ'O 


31 






<ii-3 




22 




im 


Feb. 4 






<I27 




26 


Ji^^^ 




7 






<I2"5 




28 






9 






< 127 


F«U 








'5 






<I2'I 










16 






<I27 











^^^^^^^H 


^^^^^H 


^B 


B 


■ 


^B 


^^^^H 


^^^1 


^^1 




■ 


►ec. 1906. 


Observations of XT OemiTwrum. 


123 ^H 






Table I. — eotUinu^. 




^H 


DaU. 


TtLfowar. 


lul«tTod. 


DbU. 


T«). Power. 




>859- 






iS6a 




^^1 


Mat. 2 


H 118 


<I3*5 




Hazimuni h«r«. 


^^1 


7 


H 50 


<I3'0 


Aug. 


32 


H 50 


< ^^^1 


30 


SL 50 


<I2'5 


9epL 


13 


H 52 


^^M 


M»y 3 


II 


<I2-S 




IH 


tt 


^^^1 


12 


SL 74 


<io7 




2S 


H so 


^^M 


14 


■• 


<io7 




30 


SL 2D 


< ^^^1 


16 


SL 50 


<iro 


Oot 


2 


U so 


<ii« ^^^1 


31 


SL 74 


<nx) 




3 


H 50 


^^^1 


n 


SL 50 


<II'0 




II 




^^^1 


' Aug. 29 


n 66 


<ia*4 




20 






Sei't. 4 


SL 74 


<I2'I 


No?. 


1 


H so 


Vav. 7 


n iis 


<i3'o 




15 


„ 


^^^1 


21 


H 50 


<ir8 




22 




^^H 


1 38 


n 50 


<i3'o 


Dec. 


20 


B 40 


^^^1 


30 


H 118 


<12'9 








^^^H 


Dec. 1 


• 1 


<i3'o 


1S61. 




^^H 


3 


tl 


<I3'0 


FeU 


9 


L 66 


^^^1 


5 


M 


<:i2-9 




13 


■• 


^^^1 


8 


tf 


<I2'» 




M 


D 


^^^1 


"4 


•1 


<i3"o 




16 


L 66 


^^1 


ai 


l> 


<iyo 




2^ 


'• 


<i3*a ^^^1 


36 


H B4 


<\yt 


Mw. 


14 
18 


II 
D 

ii 


<i3'o ^^H 
< JSX} ^^^1 


i8«o. 








u 


L 66 


< ^^M 


Jul 6 


H 84 


<ir3 




JO 


• > 


<:i3'o ^^^1 


16 


n 


<I3'0 




3» 


II 


<i3-o ^^H 


so 


II 


<I30 


Apr. 


I 


tl 


<I3'0 ^^^1 


'7 


It 


<i3-o 




a 


,, 


< 13-0 ^^^1 


3» 


It 


<12-8 




S 


„ 


^^^1 


F«b. 9 


E 66 


«[a'6 




9 


U 


^H 


k " 


H 50 


<130 




14 


11 


< ^^^1 


1 >9 


II 


<i3'o 


&U; 


16 


L 66 


< ^^^1 


1 '' 


H 66 


<I27 






Maximum here. 


^^1 


1 "^ 


H 50 


<ia7 








^^^1 


■ Mkr. 9 


8L 52 


<ir3 


Oct. 


10 


L 62 


^^H 


B 


T4 


<l2-3 




27 


SL 50 


^H 


K 




<I30 




19 


L 62 


<i3-o ^^M 


^^^^^H 


K 


•e 1 j-O 


Not 


>S 


L 77 


^^^1 


^^^^^1 


m 


<i3*o 




16 


h 61 


< ^^M 


■ 


k 


^^*7 


^ 


18 







134 



Prof. S. M. Turner, Pogson's 



ucvn:. 



I 



Hui 







Tahlb L- 


-Am/in«kd. 






rwt«. 


Tal. Power. 


Icturml. 


IM*. 


TeL Povar 




i86t. 






1863. 






Not. rj 


L 77 


<i3*o 


Oct. 


7 


SL SO 


<WJ 


Dec. 3 


L 62 


<i3-a 




2S 


L 66 


-ciri 


6 


SL 50 


^127 


Nov. 


11 


II 


<i3v 


9 


L 77 


<i3"a 




22 


,, 


<u< 


14 


L 6> 


<l2-8 




26 


,, 


<u-S 


<7 


*i 


<I2-S 


Dec 


7 


,, 


<i3i 


n 


L 77 

tfAxiamm here. 


<i3i 




32 


Itlaxtmutn here. 


<117 


iS6z. 






1S64. 






Jul. 30 


L 66 


<i3"o 


Jan. 


2 


L164 


<i|*5 


Feb. 8 


SL 50 


<I2*0 




as 


h 63 


<us 


Mar. as 


„ 


<I2'5 


Feb, 


'5 


t« I .1 


<i3'o 


»7 


L 66 


<I3*0 




29 


<t3*9 


Arr. 4 
9 


11 


<I3 

<I2 5 


Mar. 
Uav 


5 

25 


(t 


<I2'1 

<I3B 


J7 


(t 


<I2'9 






Mtximiiin hero. 




33 


n 


<l2-5 


Oct. 


4 


L 164 


<I3^ 


24 


>l 


<I3'0 


Dec. 


6 


L 63 


<13D 


May I 
20 
23 

OeL 6 


tl 
■ I 
It 
It 


<i3*o 
<i3tj 

<I3>3 
<12*7 


1S65. 
Jan. 14 


Maximum her*. 
L 63 


<J2'J 


16 


L 62 


<I27 




25 


■> 


<i3i 


Noc, 4 


SL 74 


<ir5 


Fob. 


4 


SL S2 


<ii-j 


9 


SL 52 


<ii"o 




14 


SL 74 


<IJK 


CO 


L 66 


<ii7 


Hu-, 


25 


SL 52 


<«•; 


»S 


n 


<i3"o 


3 


•• 


<I14 


Deo. 31 

1S63. 
Jiti. 6 
12 
21 


tl 
II 
It 


<I2'8 

< 12*5 
<i3'o 


Sflpt. 


19 
21 

24 

26 


L 63 

ri 

M 

Uftiimum here. 
L 63 


<:ii7 
<13"0 

<'»7 


Feb. 6 




<ia-8 
<i3'0 


Oct. 


30 
10 
1 

4 
10 


L 70 
L 63 


<I3V 


S3 

Mar. 7 


11 


■CI3-0 


No». 


*t 
L 164 


<I3'9 
<l»7 


«3 


^^^^ 


V 


lee 


30 
t 


L 63 


<124H 



Uay S 




I 



Observatimts of U (HmMuyrwrn.. 



6. Comparison St<xr$. — Pogson kept a small MS. book labelled 
*' Comparison Stare for Variablea," in which usually tlie upper balf 
of the page i» devoted to tho^e tor one fttar and tlie lower half to 
Ihoae of nnother. Thus p. 17 is shared by R Cancri and V Ilsclum. 
Hut the whole of the opposite page (16) is devoted to the stars for 
V G«minorum, and some of the records are squeezed in margins, 
having obvioualy been added. The stars first adapted were a, b, 
d, e,/, g; then <•, h, <?, I, m were added in the margins, and Hnally 
new measures of «, /, (f, h and the star 71 were squeezed in. No 
dates are given of the septtratc ubsenrations. When ten measures 
of any star had been secured, the mean was taken, and the star was 
theDccfurward deuuted by this magnitude, ouiittinj;^ the dedmal 
p4iint. Thus star a is often callod 88, even in the original noto- 
booka ; and wliere it is called a in the notebooks it is copied out as 
83. Sometimea the adopted magnitude of a star has been changed, 
and thus the same star is dmj^nutc-d by different numbers at 
different times. Thus the magnitudes of b and c wore at first 
taken as 9*3, and both stars designated by this number. Later the 
revised magnitudos were found h = 92, i- = 94 ; and ultimately they 
were again change<l to 93. Equco the recurd oj Vie original wjie- 
hook is given iji Table III. whenever pumble; but in some cases a 
doubt LB inevitable. The original notebooks are not available 
before 1S59. S^rnh has been made for thera, by the kind per- 
mission of the Itadcliffe observer, at the Radcltlfe Observatory, 
but so far without success. 

There are some curious corrections and deletions, notably in the 
casQs of stars e, g, and k, wbcre ten large rea^iings have bean 
systematically struck out ; but there seems to be no reason to 
restore them against Pogsou's owa judgment, though they are 
added at the end of the table. Those for € all come between the 
first and second aeries retained : thusD for g and h are interspersed 
among the separate membors 01 the first set of ten retained. 



[Table II. 



m 126 


Prof. H. S. Turner, Poyson's LXVli. 2, 






t 


Taulk II. 






f 


Pofson't Obftrvation/i of OomparigvK Stan, 






c 1 


b 


« 1 


d 


< 


/ 




yo 


9W 


n 


9'5 


9-S 9-5 


10*3 


10*2 


II'I 


IO-8 


11-4 


ui 11 




8^ 


87 


94 


9-3 


95 


9-3 


lo'a 


10-4 


10*8 


lO-S 


u-c 


ir] 




87 


9*0 


9-1 


9-6 


9*0 


95 


lo'a 


10*4 


iixt 


107 


II-3 


tn B 




a-9 


8*7 


93 


90 


9'4 


9'3 


IO-4 


10*5 


10*9 


IO-8 


11-4 


If '4 B 




9« 


S-8 


g-i 


9*3 


95 


9*5 


lo-s 


10-3 


10*6 


lo'9 


ii-o 


Ml a 




8-6 


8*8 


9-2 


9-3 


9'3 


9*2 


10*1 


10*6 


io*s 


II-o 


tl>3 


ii-||k 




8-6 


«7 


9*3 


9*3 


93 


91 


io*3 


IO-5 


1 0*9 


IO-6 , 


"•3 


11*5 a 




-9^ 


87 


91 


9*1 


9*5 


9-0 


10-3 


10*3 


II'O 


Jo-S 


it-6 


in B 




8-7 


8*5 


9-3 


94 


9-2 


94 


10*1 


10-5 


107 


to-6 


ii'a 


111 n 




9« 


8-5 


9i 


9"4 


95 


95 


10*4 


104 


10*9 


""■' 


11*3 


11-4 « 

— h 

11-33 If 


^f H«in>i 
■ Ado|)tcd 


8-84 


874 


9-24 


9'28 


9'5' 


9-32 


ID'36 


]0'4i 


10-84 


1077 


II -as 


S 


K 


9'3 


9'3 


10-3 


lO-S 


in 




L 








1 




■ 




r 


A 


( 


m 


II 


• 


« 




lau 


117 


ia-3 


11-8 


13-0 


11*3 


ro*o 


11*1 


12*5 11 




^^H 


I2'0 


11-6 


la's 


«*5 


13-0 


II'J 


10- 1 


10*8 


IS*I 19 




^^H 


I2D 


11-3 


12-5 


12*0 


13-0 


11*3 


10*3 


10*9 


ia'3 P 




^^1 


120 


13V 


12-3 


12-4 


13-0 


ITS 


lo'a 


ll't 


la-a fl 




^^H 


■ at) 


11*9 


13*4 


I3'3 


13-1 


11*3 


10*3 


it-5 


la-a e 




^^H 


ia*o 


li'9 


ia-0 


13-3 


131 


"■3 


10*3 


ii*« 


ia*3 « 




^^H 


ir? 


11*9 


ia*o 


J2'3 


13-0 


"S 


lO-l 


ira 


12*3 s 




^^H 


13*0 


13*0 


1 'a'4 


13*5 


ia*9 


11*4 


10*2 


II'O 


I3'« C 




^^B 


11-9 


irS 


ta'i 


13*1 


13^0 


n-4 


tO-2 i| ll'l 


ISI 1 


i 


1 Meuin 


■ I'D 


n"9 


ia'3 
laa^ 


13*5 


la-^ 


113 


10*1 


IfX 


-i 1 




^1 


11*90 


11*83 


13*36 


13x90 


11-34 


1 


H A'lopt«>d 


1 


"9 


ia'3 


IJ-o 


1 


i 





Dec 1906. Observations of U Qeminontm, 



127 



7. From eXHmioation of Table II. the foUuwing identifictitioDi 
are soggested for the numbers by which Pogsun iDdicat«8 stars : — 

88or 89 = a; 93 = 6; 93 = 6 ore; 
94 = e; 103 =n; 103 = ^; 108, no, or 1 i»=e; 
iia=/j 1 13=/ or m ; i i5 = ?h ; 119, 130, or 121 =(/; 
123, 134, or I25 = A; 130 or 131=/; 137= I 

PoKSon'fl diagram is reproduced with this paper, an>l tbe 
approximate poutionii giveu below uxe read from it. On reference 
to Mr Knott's diagram oti p. 94 of Meiaoim R.A.S., vol. Hi., it will 
be aeen that he uned practically tbo dame stars, and a comparative 
table is giveu bolow. 



«i' 



-^ 



Ml 



is^ . -trf- tr^ ^^ 



wr 



r 



'4 






*P^7 ^■ 



,^m . ^gm, ^yn, 4jrt. 



S£' 



tf" 



jy 



t« 



Of 



^~W^ p-' 



■Xi' 






138 



Prof. H. H. TVinwr, J*ogwtCt 





POgMU. 










DIacruii. 








ITa 


KJL Dm. 


Utttf. 


' 


>Mt 


Var. 


b m ■ , . 

7 46 48 aa « 


U 


tF 




88 


46 49 22 2 




a 


8*6 


9a 


48 19 32 15 




e 


9-3 


94 


48 S 22 13 




t 


9*3 


103 


4S J* " 37 




tf 


103 


loB 


46 aa 23 13 




r 


lo'6 


i'3 


46 48 23 aS 




/ 


111 


119 


47 6 w «3 




9 


la's 


»3 


46 53 « »7 




k 


laj 


130 


46 53 22 21 




k 


<3'3 


"3 


46 5* «2 17 


M 


... 




im 


46 a aa 38 




• M 


... 


137 


\ 


k\ 


I 


"37 



R.A. 


DM 


b ■ B 




7 47 5 


aa ao 


7 47 i« 


aa t 


7 4831 


»a 13 


7 48 »5 


>a II 


7 45 53 


M 3* 


74fi3i 


xa 10 


7 47 3 


aa a& 


7 47 «* 


33 ao 


7 47 w 


» *4 


7 47 10 


83 fS 


... 


-. 


... 


... 


7 47 


aa 13 



8. This bfling pnmued, it seenu the b«Bt cotuse dow to giT* 
simply thi ori^nai nottbook reaml^ uui this hu been ilone in 
Tftbltt III. below. Aftar 1665 the occsiions when the tlu wu 
looked for without suoeeM or* cumpWBtiTeljr fow, aod bart ban 
given in the onlinary form. 

Tasui IU. 

ObaavaUem ^ U Qtmuwrum »mr Morimiim 1856-1865 ; mitd tXS 
oteiPMtfdiM 1866-1SS1. 



Owl* 


t 


1 


Oamr/hiUont. 


IkiU. 


2 




OMVMlMi^H 


18561 








1857. 






■ 


Mar. 26 


f. 


1 


Kst.97>88 + 7 
=93 + 3-93+" 


Apr. 14 


E 


54 


l03 + 7=lio-^n 
= 113-16 


17 


B 


54 


88-<- t3«93-f8 
= 93t6«ll3-6 


'5 


K 


95 


iio + 3>ii3-*2 
= iai -7 = 114-10 


89 


E 


54 


Eit Ill>s93+17 


16 


K 


95 


iat = t24-3 J 










18 


E 


9$ 


lavia. = < Ij-S \ 


1857. 








Oct. 30 


AI. 


9> 


97 


Apr. 7 


E 


95 


88 + 8 = 93*5 








^ 


8 


■ 


Vt 


= 103-6 
88 + 8 = 934-5 


1858. 






m 








= 103-5 


Ko*. 17 


8L 


50 


93+ 5*"^ -3 


11 

L. 


K 


54 


S8+6 = 93 + 3 
"103-7 


18 


BL 


JO 


103+7=110-} 
= 113 5 



^KDec 1906. 


Ohdervations of U Gemi7U>runt. 1 29 ^^H 






Tabu III.— amiinued. 




^H 


^V Date. 


D 

H 


t CoaafMriMD*. 


DaU. 




i 

* 


Coupariiou. ^^^^^1 






a< 








a. 


^^^^^^1 


H^>859 






1S62. 






^^H 


^beb. 16 


H 


50 (i+6=i=e-a 


Jan. 


2 


SL 


50 


88+2=93-3 ^^^1 






=rf-8 




4 


6L 


50 


^^H 


1 


SL 


85 o+3=i-j»c-a 




s 


SL 


50 


8^+7=93+1 ^^^1 


^1 


H 


SO a+2=b-3=o 










^^H 


H 


H 


50 t+3=e+l=d-7 




6 


SL 


50 


88 + 10=93 + 3 ^^^H 


H 


H 


50 t+6=c+5=(i-4 










^^^H 


1 


E 


50 r+is=rf + 6=:/-4 




8 


L 


63 


^^^H 


H 


H 


118 f^xo-g- i^A-4 




10 


SL 


50 


^^^H 


H isfo. 








If 
18 


SL 
L 


50 
77 


130+3 ^^^^ 


^■Apr. 23 


SL 


50 88 + 2=93-3 












B 


SL 


50. a + 3 = * + 2^c-a 


1863. 






^^^^ 


■ 


Db 


66 88 + 6-93 


Apr. 


8 


L 


66 


94+2=103-8 ^^^H 


H 


SL 


50 S8 + 10S93 + 5 




9 


L 


66 


^^^1 


■ 


SL 


50 93 + 8 




10 


L 


66 


94+6=103 7 ^^^H 


1 


H 


52 103 + 7 = 110-2 




tl 


L 


66 


SS + T2^9X + 8 ^^^H 


■Uft7 1 


H 


52 II3 + 5-I2I-4 










^^^H 


^B 


Da 


I 121+4=130-7 




12 


h 66 ■ 


^^^H 


H 1861. 














^^^H 


^■lUj 2 


L 


66 88 + 1=92-3 




'3 


L 


66 


^^^^1 


I 


L 


66 8S + 7-92+5 
= 103 - 13 




14 


L 


66 


^^^H 
^^^H 


^1 


L 


66 88 + 4=92 




'5 


L 


66 


124+8=130-2 ^^^H 


^1 


L 


66 88 + 4 = 93 




17 


L 


164 


IJ7 + I ^^^1 


1 


L 


66 88 + 8^93+6 


Dee. 


31 


L 


66 


124+2*^130-4 ^^^H 




L 

L 


66 88^7 = 92 + 5 
66 88 + 5 = 93 + 2 


1864. 






^1 


1 


L 


66 88 + 9 = 93 + 6 


Sept. 


a? 


L 


164 


^^^H 


^H 


L 


66 88+11=93 + 8 










^^M 






= 92 + 3 




28 


L 


164 


131-1=124-5 ^^^H 


^H 


L 


66 88 + 15 = 92+13 










^^H 






= 93 + 7=103-7 




30 


L 


164 


130- 1 ^^^^H 


H 


L 


66 103+3 = 110-5 


Oct. 


4 


L 


164 


lQvifi.^<i3*i ^^^^1 


H^ 


L 


66 IiivU. = <io-5 










^^^H 




^ 


j|^^w^s<i3'i 


1865. 






^^^1 




■ 


^^H^a>:iio-s 


Jul 


9' 


L 


63 


^^^H 




■ 


^^^V>93-2 




■4" 


L 


63 


Inria, = < 12'8 ^^^H 




■ 


^^^■^ 


is written " 


Looked in T&in for V ^| 




1 


^^^^ 


\ but 

m 


die 

■' 1 


' tnoon \ra» loo briglit to net* ^^M 
[m Lot obMiratioo o( Jan. S^^^^^^^H 



^B 


■ 


■ 


JProf. H. B. Turner, Pogson's UXTil^ 


^^K 






Table lll.—cotiiiau*d. 


i 


^ 


t 




ComiMrttooK, 


D»U. 


B 

H 


I 


^^m 








I86& 




1 


^^H Apr. 


L 


70 


130-2 


Apr. 


23 


L 


70 1Z4 + 4 ■ 


^^H 


L 


TO 


94 + 3 = 103-8 




23 


L 


1&4 Ittvi*. =^ < isf fl 


^^H 


L 


63 


94+6=103 5 


Hft7 


14 


63 


63 InT{8.= <: I3"8 " 


^^^H 


L 


63 


94 + 9= '03 4 


Hot. 


3 


S 


45 InvlB. = <i3io 


^H 


L 


«3 


94+14=103+1 
== 1 10 - 4 


Doc. 


25 


s 


86 Iiivis. = < i3'5 M 


^H- 


L 


63 


124+5=130-2 


1867. 




1 


^^^^H 


L 


63 


130 + 5 


Jan. 


17 

23 


L 

L 


63 InvU. = < X3V fl 
63 Inyfa,»<i3irifl 


^^^^^ 








Har. 


8 


S 


86 Invis. = <I3'S " 


^^^H 


L 


63 


liivis. = <I2'S 


Oot. 


26 


L 


63 ravU, = < ij-D 1 


^^B 


L 


70 


lnrii. = <l3"0 


Dm. 


14 


S 


86 SS+io = 93 + s 


^^1 


L 


63 


88+5 = 94-1 








= 103 - 6 


^^^H 






= 92+2 




15 


s 


40 93+5 = 103-8 


^^m 


L 


63 


94+2-103- 10 








= 88+. 10 


^^H 


L 


63 


88+5 = 92 H-a 




t6 


s 


40 93+7 = 103-3 








=94-1 




'7 


s 


86 n - 1 =T 103 - 3 


^^^^ 


L 


63 


93 + 3=94+1 




18 


s 


86 io8 = m-5 


^^H 






= 103-11 




19 


s 


86 113 + 3 = 111+ 


^^^B 


L 


63 


94 + 3=103-8 








= 119-7 


^^H 


L 


63 


94+3=103-8 




20 


B 


86 h+i=i3o-6 


^^B 


L 


63 


94 + 4-103-8 




31 


S 


86 130+1 


^^f 


L 


63 


94 + 5 = 103-7 




32 


s 


86 I30'>-5=I37-1 


W 


L 


63 


94 + 5=103-8 




33 


a 


163 Bqaal 137 


■ 


L 


63 


94+5-103-6 










1 


L 


63 


94+7*103-4 


186s. 






^^H 


L 


70 


94+7=103-3 


Jau. 


31 


s 


86 Inris.si <137 


^^H 


L 


70 


134+6=1131 -2 


Hsr. 


11 


8 


86 Inria, = < zyo 


^^M TA. t 


L 


164 


In™. = < lyo 


Apr. 


9 


S 


86 Iiiria. = < 13*71 


^^^v 


L 


164 


130+3=137-3 




tS 


s 


86 Iiivb.= <t3'j 


W M*r. 21 


L 


63 


Invii. = <i2*5 


Not. 


17 


s 


105 137 + 3 


H Apr. 


L 


63 


Inris. Ki < i3'o 




fS 


s 


86 137+3 




L 


70 


A + 8=i30-4 


Dec 


9 


s 


86 luris. Si <. ij-j 


L 


70 


A + 3=i30-7 


1869. 






^^v 


L 


63 


94 + 4=103-5 


Jan, 


6 


L 


66 Invia, = < 1 ji| 


■ 


L 


63 


94 + 5 = 103-5 


F«b. 


20 


s 


86 93-t-d=^fn*>»< 


1 


I. 


63 


W + 7 = i03-3 
= loS - 10 




21 
*3 


8 
S 


86 93- 
86 9^ 


H ao 


L 


63 


94+itsio3 + a 

= 108-4 




24 


8 


■ 


1 


L 


70 


108+5=112-4-3 
= 115-3 


Oct. 


27 

3'' 


S 


1 



H Dec 1906. 


OA«»rva<i<»M 


0/ U Oeminorum. Ijt ^H 






TaBUB III.— cntUiuUfti. 


^fl 


^H tm*. 


^ 


> CompsrtioDi. 


Dote. 


7 


t ConiparlouEu. ^^^^^^| 


^M 






1872. 






^1 17 


s 


86 94^ist03-5 


Mar. 7 


s 


90 123+3=130-6 ^^M 


H 


s 


86 94 + 4 = 103-7 


S 


s 


90 130 + 2 = 13$ -6 ^^M 


^H 


a 


86 94-^5 = 103-4 


9 


.s 


90 =138 ^M 


^1 


s 


86 103-1 


10 


s 


go SnB]t«cted= < ]4» ^^^^H 


^1 


8 


86 103+7= IoS + 4 

= 113-2 


13 


L 


63 lDvii. = <i3<o ^^^^1 


^H 


8 


86 119 + 3=183 


1873. 




^^^H 


^B 


S 


S6 13ft t 1 


Feb. 15 


L 


Iijt1s.= <u-5 ^^^H 


^H Not. 34 


8 


86 IiitU.= <137 


H«r. 37 


L 


Ioru. = <ii7 ^^^^1 


H 






1S74. 




^^B 


^H J«a. 17 


& 


105 lnTi&.= <I3*S 


Jin. 14 


L 


106 luTU, = < I3'0 ^^^^B 


^1 


h 


66 Iurl«. = - 12-5 


Feb. iS 


L 


Inrii. = <i3-o ^^^^H 


H 


L 


t66 Invis. = <:ia7 


1S75. 




^^^^ 


^1 Fab. I 


L 


166 Ihtu. = <I37 


Jin. 15 


L 


63 8S + 8=94 + 4 ^^^H 


^1 


L 


66 lDvi9.= <iys 






^^^^1 


^H 


L 


66 Idtm. - <I37 


16 


L 


63 88+10 = 94 + 4 ^^^^M 


^1 


S 


... Iu7is. = <i4'o 






^^^M 


^H 


s 


105 93 + is=i03 + a 


18 


S 


73 88 + 10=94+5 ^^^H 






= 113-9 






^H 


s 


45 89 + 5 = 9i 


19 


L 


63 88+13 = 94+5 ^^^1 


^1 


8 


45 89 + 3=91 


10 


8 


73 94 + 6=102-3 ^^^H 


^1 


8 


45 89*3=9a-a 
=94-4 


32 


8 


73 94+7 = t03-3 ^^^1 


^1 


S 


45 89+5=91 + 1 


34 


S 


73 108+1=113-3 ^H 






= 94 


26 


s 


loa 123 + 6 = 130-2 ^^^^M 


^1 


S 


45 93 + 4 = 94 + 3 


37 


& 


I03 ^^^H 






= 103-9 


Feb. I 


8 


99 130+7-137-3 ^^^B 


^H 


8 


45 93 + 5 = 94 + 2 
= 103 - S 


? 


S 


I30 < 14*5 (siupeot«d) ^^^H 






D«c. 18 


L 


67 < i3'o ^^^^H 


^1 


8 


4S 93 + 3 = 94 + 4 
- 103 - 8 


1876. 




^^M 


^^ 


8 


45 93 + 6 = 94 + 4 
= 103-7 


Jan. 13 
1877- 


S 


lDvis.:=<l3-o ^^^^H 


^^ Mar. 1 


6 


45 93 + 7=94+6 


Jail. 4 


L 


IhtU. = < ^^^^^1 


^B 




= 103-6 


Uar. 11 


S 


73 < ^^^H 


^m ■ 


S 


45 93+8=94 + 7 










= 103-4 


Ua; 9 


L 


61 < ^^^^^1 


1 ' 


a 


45 9i+i2=.94+io 
= 103-3 


Oct 13 
i88a. 


S 


^^^H 


■ ^ 


s 


45 93+ '3= 103 -a 

= 108-6 


Jan, 2 


S 


]itvui. = <i3'o ^^^^1 


■ s 


3 


45 103 + 3=108-4 


iSSt. 




^^^B 


L. 


8 

ft 


90 iQS+4 = /ij + i 


Afar. 23 


L 


6s ln'ru.= <lVT ^^^^B 



132 Dr Russdl, Stellar ParaUtas Papers^ No. j. LXTQ.; 



Stellar Parallax Papan^ No, 3. 

The Parallax of Hight Stars^ from Photoyraplis taken at 
Catnbridye Ohnerratory by Arthur R. HinkSf M.A., ami 
writer. By Henry Norris Russell, Ph.D. 

Tbo foUowuig results are derived ftom plates token at 
bridge by Mr A. R. Hinks and the writer, and iueasui«d 
disciused by the latter in the course of liis work as 
assistant of the Carnegie lufllitutioo. A full description of 'Sbt 
methixlB of observation and rwduclion is given on pp. 775-800 
the Monthly SoHea for June 1905 

Table I. gJTea the relative parallax of these atara with 
to comparison stars averaging about the 9th magaitud«. The hd 
column but one gives the number of (xuu[>ari8on stars for md 
aehes, and the preceding column the number of plates in the Berifl&' 
The same comparison utars were nseil fur Noa. 2 and 3, whiei 
appear on the same i)laCPA, and similarly fur Nos. 7 and 8. Tfci 
two bright tttaru ^ and tj Casfiopeiie were pbotographeti with > 
colour-acrvcu, which reduced their photographic brightness t^ 
about 5^ magnitudes. 

Tabi.k I. 



No, 


(tur. 


K.A. Doc. 

TI)0CO 


M>i|i. 


P.M. 


Piu»llu. 


Platoa. Ctanr 
Stan 


1 


jB CaaaiopciaB 


3-8 


+ SS^afi' 


a-4 


o'SS 


4-0'OS3±0'OO9 


5 


9 


2 


Oroomhridge 34 


I3'6 


^ 43 27 


7-9 


2-82 


+o-a50±o-oi3 


6 


9 


3 


36 Andromeda 


13-5 


+ 43 IS 


5*9 


o'os 


-0-O26±0-O4l 


6 


9 


4 


% CuHinjidfii 


42-9 


+ 57 18 


3-6 


I'M 


•>-0'lSSj:0'031 


7 


8 


5 


flCeti 


2 I4'3 


- 3 26 


Vsr. 


0'24 


+ o-i36±o-03S 


7 


9 


6 


Lftlande 25372 


13 407 


+ 15 27 


8-5 


2*32 


^0'22I±0-0I9 


8 


9 


7 


Betlln H 5073 


14 21*1 


4-S4 6 


9-0 


1-42 


+0-067 ±0*040 


7 


7 


S 


Berlin U S073 


14 3I-I 


-{-24 6 


9« 


1*42 


+ o'ooo±o*oa9 


7 


7 




The Inst column gtveg the probable error of a co-ordinate of 
ea«h star, rebutting from nne plate, as derived from the leaa- 
squaro solution for the j^arallax. If we divide ttie stars into thm 
duses according to thi?ir effective phutogmphic brightness, w 
have three stars with faint images, Nos. 5, 7, and 8, four pi 
moderate brightness, Nos. 1, 2, 4, and 6, and one star, > 
whose imag(-s are somewhat large and diflfuse. The avenge v > 
of the probable error of one plate for tht-sc three ffroupe »tt 
±©"■065 fur the faint stars, +:o°'o27 for those nf 
ne&s, and ±c''o69 for the bright «tor. 

This emphasint^e the importance of proper 
wish t<) secure highly nccnrate plates. It w 
if the exposurea for tlie three faint stars 
usual length (Hve minutes), had been 1 



[Dec. 1906. 



The Parallax of Eight Stan. 



^ii 



Stars brighur than the 6th ma^iuide were, aa a rule, excluded 
from our working list, unless ohserwd with a oolour-screen. The 
[large probable error for No. 3 <which wan uoly moasured because 
[it happened to be on the plat&K of No. 2) justifies thu course, 
[while ihe two good results obtained with the coluur-acrecn ahow 
[ttiat it affords a aiitisfactory way of avoiding the over-ex iKwure 
Iditficiiltj. 

Several of thcM utaTS have already t)e«n observed fur parallax. 
^Tho results, so far as known to the writer, are as follows : — 



\fi Caasiopeiu*. 



3r= -f o"r5±o'o2 
IT— +o'i4±o'03 

ffsa +0*lQt0'03 

[Grooiiihiidge 34. 

w= +o'29 + 0*025 
f= +0*31 ±0*034 

\.if Cauiopeite. 

ir-x +0"IO±0'O5 

«■= +0-37 ±o-io 
v= +o'ao±o'o6 
jr= +o'i4±o'o8 
w= +o*44 ± 0*04 
ir= +o'34 ±0*04 

V= 4-D'l8±0'OIO 

Lalande 25372. 

r-= +0-43 + 0-065 
»" +OM7±o*043 



Pritohanl, photo^Taphy. 
Koatinsky, absolute dccliuatious. 
Flint, meridian transits. 



Auwcn), difT. of R.A., micrometer. 
Flint, transits. 



from distances I 0. Struve, 
„ p08. angles j filar micrometer. 

from distances I Schweizer, 
,, pos. angles j filar micrometer. 

Diivis, from RutherfunI photographs. 

Flint, transits. 

Peters, beliometer. 



Flint, transits. 
Elkin, heliometBr, 



Flint's results have received large corrections for systematic 

personal error, and the Rutherfurd photographs nf yj Cotwiopeice, 

^Mb^ taken at widely dilTerent hour angles, are affecU-d to a con- 

laiderable but unknown degree by atmospheric diiipereion. U we 

reject the last, give Flint's values lialf weisbt, and the heliometer 

iteaolts double weigbt, we obtain nieau values for the parallax of 

the foar stars, from which the results of the present paper differ 

by o'-o5, o'"05, o'"oo and o'oo respi^ctively. 

If we a&Eume that our resultt are responsible for two-thirds of 
di>cn.- policies, their average probable error would he ±o"'02o, 
affects of any syftomatic error. It would therefore 
: Itttter must be very »>mall. 

the residuals for the eomparifton stara shoirs 

Iwiee of parsllax or proper motioa except for 

rhich ap{>ears on the plates of No. 2, and 

motiuM of about +o"'3 in z. By 

lU&JE of this star should be about 



134 ^^ Ru&adi, Stellar Parallax Paperv, No. 3. LXTH: 



o''029, while the average parallax of otara of the ninth mag 
« o''oo6. 

We may thercforv a&sumu that llic uieau i^mrallax of our 
perison stars 18 o' "009 for No. 3, aud o'"oo6 for the rest of 
aerieft. Ad<ling thiH U) thi*' relative pAraIlaxf« of Table L, 
obtain from the resulting absolute (jaralUxes the following; nil 
of the aUMtliitti QjagiiiludKs of the vtant {i.e. tlieir rua^itadw: 
at such a diatancf- tluit their parallax vraa ^''to) and of 
light in terms of the Sun's, and thuir velocitieB at right an^M 
the lino of sight. 

Groombridge 34 and if Cassiopeia are double, and data 
given for both coiuponenta, and for Mira at maximum (mag. j'; 
and miuimuiu (9'5). 



Ma 

I 

3 



SUr. 

Cwsiopeiii; 

Groom liridgc 34 

Ti Oajraiu]!cia! 
«Oeti 

Laliiiido 35373 
B«iliii B S°7* 
Berlin B 5073 



A 

B 

A 

B 
Max. 
Mil.. 



Tablk II. 

AtMotnto 
2-1 

ro-o 

I3'6 

5"i 
9-1 

43 
lo-j 
10-3 
(7-0) 

u-0 



Ughl. 
23* 

0*016 

0*0015 

"•5 

0*04 

3-0 

0-ori 

OMII 

(0-25) 
(0-33) 



LVoM-valcMl^. 



Ast. unite 
per rear. 

6-3 



is' 



lo'g 



6-3 



»7 



lO'a 



(35) 






3* 



49 



(170) 



X08. 7 and 8, which are 45* apart, linve a common proper 
motion,* and are no doubt pliysically connected. The mean of 
the observed parallaxes, +o'*033 to'-oss, has therefore been 
taken &f« tiie trUL^ value for hotli stun>, but it is clear that liUb 
nrliance can be placed upon the numbere calculated from it. Ii 
is, ho-wever, probabla that these stars are fainter than the Sun, aod 
are niuviLg across the line of sight faet«r than any of the otbns 
in the table- 

The negative result for 36 Androniedce is leaa than its prohabb 
error, and indicates that the parallax of thie star ie insenatble. B 
was measured because the Bonn A. G. catalogue gives it« pmnir 
motion in R.A. as +o*oi6, wliicli is ten times the true value, IJ 
its actual cross-velocity is equal to the mean of thnt of the othtt 
stars (exchuUnc No(*. 7 and 8), its parallax would be ouly d*'M4r 
It is double (O^ 5), and it£ loth magnitude conjjMtnios ' 
fixed in 340*, t'-i — which should be the case if it« 
small. 

17 Caastopeiee is a well-known binary. Ftf 

• nelUmy, M. A*., Dec. 1899, p. |: 
t J/«m. R.A.S.. Tol. ItI p. 16. 





I906. 



Thi Parallax of Evjkt Stars. 



'35 



re have a=S''5i Pssjj yeara, which with onr parallax gives 

[the mean diatauce of the componeiitB as 44 a8tronoinica.l unite. 
rTbe actual dislance varit;» from 58 to 30^ and tim combined mass 
1*6 times that of the Sun. According to Lewis, the bright etar 
twice aa massive as the fainter one, so that it very nearly equals 
|the Sun in ttinHS m well as in light. 

GrooTiibridgo 34 has a physical companion, which waa measured 
Iby Auwers • iu 1865, and i« nhown on some of the plates of the 
[present scries, as ia atao a fainter compunion nearer the priudpal 
Btar. 

The writ<>r'8 meaauros, made this month with the 23-inch 
equatorial of the Flalated Observatory at Princeton, show that 
this is only an optical companion. They give, for the co-ordinates 
of the companions, relative to the principal star, 











s 




ti»-S 






> 




v 


z 




V 


A u went 


1866-23 


+31 -a 




+ *3-4 








Plato 391 


19U4-98 


+32-3 




+ 21 -6 


+ 32^ 




-I3"3 


H«l8tlHl OU. 


19067S 


+ 3»a 




+ ai'S 


+ 26-6 




-14a 




Proper 


motion of A 


in 


iularrkl 


+ 51 




+ 07 



Tlii^ companion alforda an unusually |{0od opportunity for the 
micrometric dctertnination of the parallax of the other two stars. 

The actual separation of A II is at leaxt 150 astronomical unite 
— four times that of i^ Casaiopeiis — so that wt- may expect the 
period of the sysleni to be some thoii.sandfi of years, 

Tl]C reiiults for Mira are also of interest. If thu other long- 
perio<l variables resemble it, and their maxitnutn rather thaa their 
minnnum light ia eoniparablo with the Sun'a, tho brighter ones 
must have easily measurable parallaxes, and it would pay to observe 
them. 

Canipbell ami Stebbins f find that the radial velocity of Mira 
is constunt, and equal to + 63 km. per sec. As ite cross- velocity 
is oaly 8 km., it is moving' almost directly away from us — in a 
direction making an angle of only 7* with the line of sight. 

If the present value of the parallax is correct, it follows that 
>[ini was neareflt tho Sun aljout 1 10,000 years ago. It was then 
in Ursa Major, and had a parallax of 1 'i and a proper motion 
of 15" per annum. If its intrinsic hrigbtnesM varied hetweeo the 
Aame limits as at present, it was of the 5th magnitude at minimum, 
and at maximum wa^ as bright as Sirius. 

Ws are due to Professor l/»vett of Princeton for 
' to continue the work here. 

vlinAktuf. der WisMMtrhnfUn, 1867, \*. 23, 
•wwif, vol 18. p. 341. 



I Mr Ctnotll, ffanstetn*8 Edipsi at Siiklaslad. LXm; 

llarateen'n Edipue at StUda^tad, 1030 Auf/ust 31 
By P. H, Cowell. 

The record states tliai the eclipse occurred during the 
Stiklattbiid at which Oiaf the Fat was killed, and the date 
to the battle is 1 030 July 29. There are two roaitons for sapi 
this dat« to be in error: the narrative mfliitions a dark 
following the battle, whereas on July 29 the aim never ginb'l 
much as 9* below tbu horizon of Stiklastad ; also, Olaf waa 
ieed, and July 29 became his festival .-ind in time the 3uppoMd< 
of hia death. Now Augu-st 31 was already at that timo 
fco another saint. The foregoing argumeiittn are Hansteeni 
JVocA. Ergauzvn'jfihfift, p. 49), I>r Dreyer {The Ob»cri 
October, p. 363), quoting Prof. Kotirad Xlaurer, decides 
later date for ihe buttte. Hti^ ai>;umenta, as far as they are 
OD the day of tiie week, d« not appeiir to me concltisive, as 
chronicler may eafiily havf> coitnted backwards. But in aor cut 
wo hare a description of a total eclipse, that it was beyond ibi 
power of the chronicler \m invent, and the eclipse ia stated to ban 
occurred at SCiklaiitad. 

The eclipse bos therefore been worked up. Considcriog in 
comparatively recent epoch, it might have turned out not to difr 
criminate between the preeent tahiea and my formul«p. The thj 
contrary is the casu. My furuiulie leave 3" *>i the northern end 
of the Sun's diameter uncovered (indicating the poasibUity of small 
errors that I am <iuite prepare<{ to admit). Hansen's tables and tbi 
pte&eut tubleH, which are practically tho same for the epoch 1040, 
shift the Moon 35' further south relatively to the Sun. The ]ff» 
altitude of the Sun makes tliifl oorruupond to about 100 milei ob 
the Earth's surface. 

Outline of CaicuIaHon$. 
t- -7-69303= 1030 Aug. 3i+a8'-53G.M-T. 

^=386 12 418 L'=i65 o 9'8 

<g= 8a 35 372 ic' = 366 18 7'l 

-0=207 10 12-3 

Inequnlitien of Moon's Longitude :— 

A. Solar terms over ao - t6 7527 

a „ 1 35- 69-8 

C. „ 015- 5-0 

Figure of Kartli terms + 4*9 

Moon's Latitude and Sine Ftirailax : — 

A. Solar terms over 10 +3 0895 +3 50c 

B. „ 055 + 27-0 + I 

C. „ 005- lo - , 
Figure of Earth terms - 3*9 



Dae. 1906. Mr A. C. D. Crommelin, Hailey's Cornel, 137 

MovetnentR in Jalion cfinlury 7 10* : — 

In geocentric olongation in longitude j6Si'6 
In geocentric latitude '^5 '3 

Stiklastad 11* 35' £: 63' 38'-8 geocentric latitude; i-p 

■» o'ooz68 
Parallax in longitude +2io'*7 ; in latitude -3132" -8 

MoTementa in Julian cenlurj -r lo*^ as seen from Rtiklastad : — 

In elongation in longitude 14803 
In latitude 44*5 

Hance if 0-09AF, AD are tbe corrections reijiiired by the latitude 
and ditTerence of longitudes, then the latitude at apparent con- 
junction in longitude in 

- 8' + 009AF -- 003AD 

Tbib difference uf apparent si* mi-diameters ia about 5'. 

^H It ia well known that Dr A. J. Angstrom publidfaed in 1862 
^^ a pi^r entitled *' Sar deux indgalit^ d*une grandeor retnan^nable 
dana les apparitions de la com^te de Halley " (Acted de la 8oci«^t<!^ 
royali) des Soieoccs d'L'psal, Si^r. 111., t w.). In this paper he 
diacuBBBA the observed perihelion passages, as detormineU by Dr 
Hind, from bo. 11 to a.d. 1835, and dedttcot the mean period of 
the comet, 76*93 year*, this period bdng affected by two large 
inequalities of amplitudes i"5 yeors, 2'3 years, p^itioda 2650 years, 
782 years. U)j hae found theoretical argummits which will satisfy 
these periods, vix. 13 <f 2 2t , JJ -I- T? - 9 1^, where thu symbols 
denotxC the mean annual motions of comet, Jupit«r, Saturn. The 
amplitudes have beeu obtained by obserratiou, and in no case 
does tlie error in the fonuula as compared with the observed 
time of perihelion oxi-eed i year ; in most coses it is lees than 
half a year. T)r AngstriJm docs not claim that these two nre the 
I only inequalities, merely that they are the most important ones. 

^H I do not think it in so ^eneraIly known that the time of the 

^H next perihelion pnaiuige, as <Ieduced from Dr .^ne^trom's curve, is 
altogether different from that published by Count de Puntecoulant. 
I deduce from the curve i9i3'o8 fur the time of the next passage, 
wberaas that given by Count de Font^conlaut is i9io'37, a dis- 
cordance of 2'7 years. 

We are not, of oourse, justified in assuming that M. VoTil^cou\tL'ti>!« 



iVoffi on tlif! ApiJToarhinij Reium 0/ Htillty's Comet. 
By A. C D. Crommoliu. 



138 



Mr A. C. D. Crommeiiit, Jn'oU on the LXTIL 2, 



remit is flrroueoua, soleljr faecanw it diffen from Dr Auf(»troai'a 
curve. For exact numerical computation is entitled to far mora 
weight than an enipincal method. But it is difficult not to fee] 
Mine nlight uoeaiiiQnw abnut the mutter, wliftt vre consider tbe 
eztrome length uid intricacy of the calciUatioua, ood the pOMi- 
bilitf that eoini- important niimericitl error iniiy have e ic aped 
deU-!Ction. It in surely a ffenJertUum that thu pfrcurbations should 
be indepeiiderktly computed, and i hope thnt w>me niatlieTnaCir-iins 
may b« actually engaged in tho work ; if not, thent is Htill lime for 
•omootie with the nece6!«ary leisure and ability to undfrtaki it. 
Before the 1 835 ret4iru ther« were at least Hve independent compaia- 
tiona of the orbit — those of Dainoiseau, Ponb'couUnt. Lehmaon, 
Roranberfter and I^bbock ; and it is difficult to understand 
vhy an equal amount of interest in not showu in tbe approaching 
return, ront^oulant's result was pobliahed in 1864, and doobt- 
lesi he regarded it a» certain that there would l>e numerou* in* 
vestigntions when the time drew nearer, ao that he may well bars 
givaii somewhat less attention to the next rt-turn than ha ^rare to 
Ihit of 1835. Thill IS home out by the fact that there art certainlj 
•ome 8h)w ur misprints (not having seen his manuacript, 1 eaiiool 
say which) in bis pajier m printed in Oomytes Seadtu tU 
I'Aeadimie, tome Iviii. Thus on p. S36 be gtves T aa 1910 
May 34'37, Paria civil tiuiv (I have verified that tbis is tbe 
oorrect value from tbe fi^urea and forniulu tliat he quoteaX bat 
on p. 828 r i» given ss May 1695 ; this is merely an error of 
oopying, smd is correctetl in a note in a subsequent nnmber of 
Compteg HeiuiuM (p. 915 of the same volume). The Oommntmmcg 
tien 7'pr^/N^ however, quut«« the latter result converted into astio- 
nomical Kckoning: while Dr Iliod [Enet/e. ffrU.^ 9th edit, vol. vL 
p. 193) quotes the former, which is unqnestionably the right one 
to take. Another case is that of the [M^rturhstion in the eccentrioi^. 
This ia made up of three terme due to Juptier, Saturn, and Cranns, 
the 9e)(anite terms and their sum being given as follows on p. 8x7 ;^ 

Aiutsuon da rmtalrMw 

A 



4 



It 



-001104550 

^•OOOO^QfaS 

TwUl, - -005655813 



ft is at once obvious that the total does not tgre* wfUi tlia 
separate t«rms as printtKl, uor am I able to eoggeet any oOBjeetuml 
•mendatioD wliich will bring them intn hnrmooy. 

This value of the total ii used in dmlucini; the eocentrictty aa 
given in tbe elements for 1910, end it is notuwurthy that liotk tlia 
•ooontricity nod ]HTiheliun distance fi>r lliat e|>ocii 'how « strikiag 
diacDTdance from those 10 earlier ap|«ritions, as thia table ehowa. 



J 



Ai)proaching JUitirn of UcUlei^s Comet. 139 



Ymr, 


GeoMttrlclty. 


PwUwIloD DiBUuoe. 


'53> 


0*9684 


0-568 


1607 


0*9669 


0-584 


16S3 


0-9677 


0583 


t759 


0-9676 


0*5845 


"835 


0-9674 


0-5866 


1910 


o'96i7 


0*6873 



^ 



The chaD;;e in the ditstaucv is » full tentb of thi; Earth's distance 
from ibu Sun. I do not ii8.<:Hrt. that «iieh n cbaiigo ie i[u{XK^sible, 
but it is certjuuly desiralile that it shonld be verified, as X stronglj 
suAj>ect that there is a confusion in the [lositimi of the decimal 
point, and thai the actunl clmuKv is uiily -^ of Lhat given. 

I huve praparttd a diayram ehowing tin; portion of the comet'a 
orbit iodide the orbit of Jupiter. The numerals I., II., III., IV., 
v., V^L, indicate the positions of .Fupitor at the instant of the 
comet's perihelion paaiage in 1531, 1607, 1683, 1759, iSjSt ^910* 
irhile the luuue uumeruls ivith suiruces A, B indicate Jupiter's 
pufiitioos when the ci>mel posiied the points A and B. The distances 
of A, B from Jupiter'n orbit ara ro, r; roapectively. The 



t«-tiD< 



av 



• tfaVj 



fau 



Orbits of Japiter, Eirlh, HiUej'i Comet, showing positioos or Jo^tteT, \%i\, 
1607, 16S3, 1759, 1835, 1910. 

W 



140 Mr A, C, D. Crommelin, LXnij 

numb«n near the numerals I., II., etc., indiuato the Jovimu 
batioQ uf the cumet'H mean anomaly lu the revolution followiogd 
passage. It will at oDce he seen that the tj^qire op|M»ite V 
abnormally large, although the approach to Jupiter frai 
closR that] for passage III. This iticreanes the suspiciun that 
fterturbatinns for tbu preiMint rovolutiuii may be too large ; ii 
in the case of the perturbation in eccentricity the suapicion 
almost to a certainty. 

I do not know whether Potiti!/coulaDt's calculations aiv still 
exiptenre; the article in C'ompfex /ietuIuM, vol. Iviii., <loes 
mention whem they are to be rouiiJ. Auuming that they bi« 
iu existence, a careful re-exam inati(;ti of all the fixtures might 
insteiul of an entirely independent computation of the jwrtorbatii 
For there is no (juwttinn whatever of Pontecoulaiit'* ahli 
merely a suspicion of possible Duuierical slips. The incoi 
that I have adduced above is of itself sufficient to denianH snek' 
re-examination, before the results can be n«ceived with conBdi 
One can hiirdly imt^^ne a greater loss of prewtige tu at>' 
than thfit irhich wnuld arise if there were a noluble error in 
prediction of this return of the comet, after tha wonderful bi 
achieved i« 1759 anil 1S35. 

Assuming that the dtite 1910 May is correct for the pei_ _ 
passage, I think the complete failure of the Angstrrini curve is 
without a warning to us. We have here a curve which adm' 
fits 35 successive [mssuges. and yet the first time it is us(d' 
predict a return it breaks down utterly, the error being almot 
years, or three times the largest pn^vinuK error. This i« a decided] 
fttartling fact, and indicaies the danger of usin^; temi:^ of > 
empirical nature in lunar or planetary tables. Where socti a 
used, it is at least deaimblo that metuiis shouUt bo provided (v 
readily elTacting their removal from the calculated positions. 



The Proper Motion 0/ Caxtor. By A. C. D. Cronainelin. 

In the determinations that have hitherto been made of tb 
proper motion of dietor, it does not appear that any effort b> 
been msde to sepamt^ true pmper motion from orbital motioft, 
the values given have merely l>ee.'n deduced from the meridia 
obaervations of the principal stur, from the time of Knidlej to lk» 
present day, on the a^umption of uniform rectilinear mnttdfi. 
This assumption was fairly justifiable for the 130 years irom 17 
t« 1S85, during which the cnrvature of the orV-ital path 
slight; it is now rapidly incn;asin>;, »n tluit the orbital mot' 
igo6 is at right iiu^les to that iu 1S20, and in a fe*-- 
accepted proper motion will become entirety erroneov 
u yet scarcely a long enough arc ci^vered by the * 
vations to make a reliable det«:rminatioa of th- 
from them. An attempt is made by Mr Lewis 




Dec. 1906. The l*toper Motion, of Castor. 



141 



tb« recently publiahod Aleniuir oil the Struve Double Stan (vol. 
Ivj. p. 2 1 5); bvit while the collection of meridian observations and 
thair reduction to a com.nion e[>uch is of great interest and value, 
it •eems to me that their deteruiinatioti of the maas-ratio (brighter 
fitor 20 timos the fainter) is vitiatud by the iuipticit a'tsumption 
that Auwers' iimper motion may be taken aa the true proper 
motion of the centre of gravity of the ayatem. I believe that it 
is the apparent resultant nioliou of the brighter star, and con- 
sequently it i» only to be expected that ite appticatioji should 
bring this star to relative rest. The int'ereoce that the brighter 
star ia far the more aiasaive I consider unaound. I bad reached 
this conclusion before I saw the diacossion of this system from 
spectrosc*«pic obRcrvationa by Dr Hobor D. Curtis in Lick Oiteer- 
vatory Bulletin 'So. 98. On the assumption that thp ttro minor 
ayatema (each stir being a it|)ectraacop!c binary) are copbciar with 
the major system, he reache;! tbe conclusion that the masfi of a^ 
(the fainter conipon^'iit) '\» 6 times thut of a^. The iuuium|)tiou is 
of course toutative, but the resulting mass-ratio i-* probubly more 
reliable tbun any that can Iia at present obtained frnm the nit^ridian 
observations. I decided to adopt it as a trial hyputhesi?, and to 
see how it would work. Uaing the Greenwich olistrvationa 
collected on p. 115 of the Stnive .Memoir, the position of the 
centre of gravity reduceil to 189a with Auwers' proper motions 
and corrections, comas out as fdltows : — 



Bpockut 
Citalufuc. 


Pm 


ttlon of CenV* of OravlQ' on I 

AMtimptlMi or :tUM«a. 


Lboab 
«.P.1J. 


•v« 


R. A. 




; 




1840 


7 


m 
27 


I 


9 
57 


5* 


16-99 


1845 






34-459 






16*51 


l8$o 






34544 






16-99 


1860 






34-SM 






»7'35 


1864 






34'49I 






t6-86 


187a 






34-490 






17-90 


18S0 






34547 






17-91 


1890 






34-601 






18-87 


190a 






34566 






18-57 



From these I deduce a correction to [he assumed proper 
tmotion of ■ . 

+ ■0016 +'041 
Auwers' value is - -0151 ■+- -079 

MewoomVs being - 0144 + 'oSa 

Hence tbe concluded proper motion of the centre of gravity of 
tbe system is -'oijs, +"-120. 

If the above mass-ratio is correct, we should e.xpect a much 
more definite curvature iu tbe fioeition of {4 than ut a^. \^ \& 




142 



Mr A, C, D. Crontmelm, 



Lxrn. 3, 



fortunate that thi« is tbe case, as olwenrmtio&s of a^ km mudi man 
Qumerotu. 1 have accordingljr nduoed the fulluwinf^ obBcrtmUon* 
of a, to 1890, with the proper mottuu -'0135, +''iio. 



ii'-ft 







Pbwittotu 0/ «« 


rrdnml tn 189ft 


T. Uftyar. 


1757 

'757 


h n 

7 «7 


34-88 
3474 


* 

57 


1 
52 


w 
31*64 t 

Adopt 34"-83 
21-54* •- -^ ■» 


Piuii 


1800 




34*84 






17-8 


0^BBIl1r{ch 


1S40 
1S4S 




34 "W 
34-94 






17*78 
1714 


It 


1850 




3493 






l6'86 


M 


1«60 




3493 






1643 


(» 


1164 




34*90 






15-86 


\ ' 


l>7l 




34-88 






1573 


' » 


iBgo 




34*91 






l3'6o 


•» 


1890 




3491 






'5"45 


»• 


1900 




34*8* 






14 '93 



TbeH have been plotted on tlie diagram ; it vill ba 1 
oDce that, omitting Viuzzi, which U dtscunlaut, the; Jo indicaloil 
a carvatura of abont the requireii amotiDt, u c«:tuipar«d vitfa Mr 
LeTis' diagram of the orhit. Hence they aiipjiort tbe adopted 
ttiass-ratio aa at least appn>zimatf>ly cortecL Obviooaly 00 eonra- 
tare would be shown if a, Imd much the greater maaa. 

Ae Castor is a Greotiwicb clock star, it would seem to be 
advisable to follow the meUxMl that hus elready beeo adopted for 
ProcjoD, riz. to nppljr a double correction, one for the pro|per 
motion of the centre of grarily^ the other for orbital motioD rQiind 
this point. 

For example, in reducing the 1890 place of Castor to 1910 wc 
shonld have to sppljr -"0135X 30-*'ii to the R.A^ and 
4-''iao»( 30 - ''56 to the N.P.D. (in a<.ldition to preceesaoo). 
Tbe Mcoiid tern in the orbital correction deduced from Mr Lcvk* 
diagmni on tbe assumption of nuue-ratio i to 6. 



Tlieaa amount to 



-'•405 -••II — 
+ 3'-6o-'-56 - 



-•}iS 

+ 3*H 



vhtnu if Anwera' proper motion were used thej^ would bo 
-••0151x30, +'079x30 --'*4S3. +•''37 

Heoee even now tbe effect of the correction ia sensible, and it 
will rai'idtj' iticmsn as iieriutron is approached. The direcUoo 
of orbital niotiun in N.P.D. will be rsveiwHl in a few yoare^ aft«r 
whieh Auwsn' and Newoomb's raluee of the motion in N.P.D. 
will become altogether erroD«oua 

This is, I beUflT^ tbe first occasion when spectraoopie obear^ 




Thi Proper Motion of Castor. 



ion? have assisted in detemtining the proper motion uf a star. 
p posaibitity uf mutual afisistance of tliia kind forms another 
fc connecting physical astronomy with astrononiy of position. 
fp^rhap^ it is as well to call attention to an erratum in Mr 
iriti' Memoir which misled me for a time nnd may mielead 



If 










■^0 












■BOo 


/ 








Hi* 








> 












'CO 


1 
t 










17 




■50, 
















45 

1 


O 










IB' 


■40 


\ 






OIBM 










1 
t 












ttf 




1 

I 

1 
















\ 


\ 










W' 






\ 
\ 
\ 
















\ 

\ 










?r' 








\ 

\ 
















\ 








zi 








1757 


& 























35*0 



3*'9 



3Ve 



K«ridtao Ol»or«&tiKuv of it, Oeminaruin (CuMr) reduced to 1890, 
with Proper Motion -■•0135, +'-120. 



tiers. On p. 21 Mr Fumer's determination ib printed as though 
3 fainter star had 20 times the mass of the brighter. Uis detar- 
natioii on p. 215 of the Memoir made the bright tttar 20 timea 
B faint, and, althoujjh the ruvetae is probably true, the two {Mige« 
ould be made consifttent. 



k 



144 ^^ Tliockeray^ Estimate of the N'amhtr of 



Sttimate of the dumber 9f Star* within Certain 
qf Proper Motion. By W. G. ThackeiBy. 



LimitM ^M 



The following data are derived from discusaioDS o( sUtiatioa 
of propur mutiuns. piibltelied (i) by Prof. Auwen in ihv intro- 
dactiuii of tliu iWrlin "A" Caulu^ao of tbo AstrmooiUcli* 
G«aBlbcb&ft aen(!«, pp. 141-143, where lie diacuasea the BnKUey 
pn^MT motion referred to here as " Bradlej." aa well aa corUin of 
his Kooe sUre referred to here as " Auwers," and thou>ifa the 8«(«r»- 
tion of the stara is not in &11 caMW identical with the K^upiitK 
adopt*^! in this {laper, it ia tiaite neAr piiough for the purpoaai 
of this [wper; {2) by Prof. Dy^on and my^eU in Uia intrixluotJoa 
to the New HeductioD of Groom hridge'a CatAlogue, n. xcii ; and 
ii) ^y tuyaelf on itome Carriugtoii profwr moiiouii, puhliahed in Uw 
present volume of the Montldy Notice*. The Btwiley obaervattom 
■xtand over the northern sky, (i room bridge's lie within 53* of the 
pole, Carrington's within only 9', and the Berlin "A"aenea u* 
within the aone of 4-15' tu +30' of I>ecliuatiou. The material 
under diaooaaion oaunot be conaidenrd to uxtend Iteyond 9*4 
magnitnde stan, bat from the reaults it would appear oa thot^^h 
the adopted percKntagtH might be uaed farther without mnch ruk 
of apjTCciuble error. 

The agreement betweou the diflerent catalogue* it eapeetaUy 
good for th^ fainter alara, and auggwu the abeenee of any *eri«iu 
ijatomatic error. 

Fmtntaft ^ »ar$ witkiu. Ctnain limita ^ CmUttniai Pnper HaOmu. 



AMhorttr. 



o" - s" j" - to" »b" - 1 



>«> 



iin.tjim»n 





HaxnJtude 1- 


4*» 






Bndlvy. 


41 aa 


\^ 


18 


711 


Oroumbriilge 


45 «t 


so 


H 


*34 




43 « 


18 


17 






lU^ttnUe S'o-5'9- 






Bndlay 


49 a6 


16 


9 


«» 


OmBfartdfp 


59 " 


U 


6 


&3> 




$5 »J 


«s 


» 


1 




HafnitDda 6x}-6-9. 




1 


Bradley 


j» *9 


<J 


« 


136; 


Orooabrtdp 


66i at 


t 


41 


1149 




60 15 


10 


S 


J 



igo6. Stars itfifhin Certain LimiU of Proper Motwn. 1 45 



Antboritjr. 


---s-j 


'-10" 


mT-w" 


>ao 


{taotStarj 




Mtgnitod 


e7-&-7*9. 






BttdTey 


55 


36 


'3 


6 


188 


GroombridgQ 


74 


t8 


Si 


a* 


1369 


Auwers . 


76 


14 


7 


a 


143Q 


CAirmgtdQ 


64 


ai 


19 


a 


114 




75 


'7 


6 


a 






llagnitnc 


eS'O-S^. 






Oroombridge 


1H 


17 


»4 


2 


940 


Auwers . 


80 


n 


7 


a 


1595 


Orrington . 


69 


19 


9 


4 


179 




79 


14 


S 


2 






Mnftnitoc 


a 8*5-9*0. 






Auwen . 


77 


18 


4 


I 


3366 


Curingtoo . 


79 


<3 


7 


I 


44a 




78 


'5 


6 


t 






Maf;uitTid(- 9'o-9'4. 






Auw«n . 


79 


13 


7 


1 


1031 


CArriogton . 


So 


IS 


5 


t 


378 



79 14 6 I 

Willi refereaoj to tie eatiraute of the oumb«r of tlie stars' for 
10 adopted gi-oupft of iiiai;nitude, SeeliKcr pvos for the counts ia 
B.lt. for the northern bemispliero the following figures : — 



Mag. I -6'5 


4, I20»un) 


6NS-7*o 


3.S87 


71-7'S 


6,054 


7*6-S*o 


11.168 


8'i-8'5 


32,S9S 


8-6-9-0 


52.852 


9»-9*5 


a 13.973 



Toul 



314.95s 



Bcale there would be 630,000 in the 

m this estimate, I have counted the 
tages in ditleroat volumes of the 
100, 125,81. 124. '43. »3»- 93. 
■5 out of everj 300 



146 Mr Tkadceray, Notes (fH aome Proper Motiont. LXVII. 3, 

<Un, aay 35 per cent, Kxcluding tbe^e, the number of atw* dova 
to 9*4 mk^Ditude would thus be some 400,000. 

The adapted values of the oiUDbenfor the different poape of 
niagnitiidi.^, and the perceotage valuee within ctrtain tiniita of 
proper motion, are given io the folloving table : — 

Hrtaange ^ Slan triihin Certain Limiti o/CenlfHUial Proptr Meti-m* m 
OnUr 0/ Ma^itmle, icith StttmaUd A'timkr a/ Start, 



Mac. 
I -4-9 


4J 


23 




>«^ 


1 


S-o-S-S 


55 


»3 


•s 




3 


610-6-9 


60 


35 


to 




13 


7-0-719 


7S 


t? 


6 




35 


«'0-9-4 


79 


14 


6 




3SO 



mHmatml Jfvmkar <^SUtn ^tkin CvtUi^ lAmiu ^ CmimmtkU Ptvftr 

MMom in Order <ff Mmfmttudt. 

I -4*9 430 2ZO iSo 170 I 

5^>-5-9 1,650 690 450 aio J 

6-0-6-9 7,>oo j.ooo 1,300 600 13 

7-0-7-9 26,250 5,950 3,100 700 35 

S^t>-9'4 '76,500 49.000 31,000 3,500 350 



3i3,ojo 58,860 14.930 $,180 40t 

From A compariBoa uf the Groombridgo and Cairiagtoo prop^ 
motioM, for tho purpose of estimatinp the effect of aceideotal 
•rror, the probable vrror of a cciit»-nuial proper motiuu in XJ^.D. 
ia ± o''8 and in B. A, ± o''9 ; thus the probablv error of a reeullaat 
cenlcnuial pmper motion ia ± i'*3. It vrould, therefore, he maaofi- 
able to infer that the nnmben oorrespondiog to these linita of 
proper mntimi would not be liable to any aerioua altaration for Uta 
•ffaot of accidental ttrror of olwervatiun. 

If the group o'- 5' ia further broki-n up it will he fimnd that 
for nil magoitudH* the itara tend to nct-umulate somewht^re round 
3'*5 M a reaultant centennial proper motion, and ibis neetni too 
la^ a quantitj t» be due to ^atamatie or accidental error. 



liott* an wtM PrcptT Motions derived from a CornporuoM <^ 
Oorringlmt's Catatof^ua vith the Grtenteieh Ptaet* /or 1900. 
Bjr W. O. Thickwa;. 

In the Oraanwich Catologue for 1900, wbioh ia now in oonna 
of coDctruction, there are 11 85 itan to ba found in Curington'* 
GSlcompolar Cntaluguii for 1855. Of tbeae etara, 94 coaunoo to 
tba (f roofflbridga-Urvauwich lyttem have been und to diwH* t^ 




Dec 1906. Mr Thacktrajft iVotei on ionu Proper MoHons. \ 47 



I 



systematic corrections opplicable to Carrin^'Vin's places to bring 
them into line with the (Jroombridge-Greenwich system, ond the 
rwnlti have been published in MontfUy Xotii-^, \xvi, pp, 320-323. 

After applying thsM corrections to the Carringtoii Catalogue 
places, proper mutiore for these 1187 stars have been derived by 
a simple comparisi^n of the Qreonwich observed places for 1900 
with the corrected Carringtori placett brought up to 1900 by Struve- 
Pctera precession conataiitit. 

Taking those stara which are <;oii]mou to Groom bridge and 
Cairington, and forming the differences of [ircpev raotiou derived 
from the tiroombridge and Carrington Catalogiie places reapecLively 
in the sense of correction to Oroombridge for every three huan 
of ri^ht ascension, we get corrections which can be compai'cd with 
the tables of corrections given by Boas in his pnper, " The New 
Reduction of the Meridian Observations of liroumbridge" uVo?»/Wj/ 
jVortcas, Ixvi. p. 513). 

Tbe tables ara given in the form of oorrections to proper 
motion in arc in t>otb elements. Boiis's corrections in X.P.D. are 
not given, as being procticaily insensible. 

Boss's corrections in R.A. are found by multiplying by -^^ the 
quantifcisB given in Table 11., Zone IV., Afonthiy Notice*^ Ixvi. 
P- 563- 

Cvmetiona to Qroamhrblg^i Proptr Motions w OrtierofR.A. 







Right Avcnflon. 


N.P.D 




Bom. 


CvTTlllgtOlcUiMiintcb. ^ 


UTiiiKUin-Un 


o*" 

■i 

1 


000 
+ •009 


t 
+ ■003 


-'•003 




-«i6 

- -OIO 

- '016 


-■003 
- •OIO 


- ^10 
-•005 


10 

<2 

>3« 
14 


-■001 

+ ■017 


+ •003 
+ ■020 


-■005 
-003 


16 
iS 

90 


+ •014 

TWO 

+ ■002 


+■013 


-•ooa 
-•004 


31 

2a\ 


-•nnfi 


+ •001 


- ■001 



k 



The agreement between Boss and Cairington is notable, and 
•hoira tbe excellenoe of Carrington's obseivat^ona. Tho «mt\\ 



I4S -Vr 7%m cJ k may , KoU* tm anw Proper MbiiottM. ixvu. 

maui diflfinvoee in K.P.D. raptaaentit but a small tytum 
diaeordanoe. 

Again afranfiinf; these Cimngton proper motiona in a 
of magnitadea aud in ocUdU of B.A., in the fl&me aMuner ai 
tAopbaA in the ease of the Graombridge Catalogne, w« gti 
foUowing tables of ntuubere and perceatagas: — 

mm i en ^ Stmn-Oat U mw i t I Pnptr MMmt m Order <^ Stmri MafSt 



S^o-5^ 


«9 


s 


s 


6 


6'o-^-9 


46 


aS 


I> 


4 


7'0-7-9 


"4 


73 


as 


«4 


S-o-$-4 


179 


131 


iS 


16 


s-s-s^ 


443 


JJS 


S3 


»7 


9-D- 


378 


30a 


56 


17 



IMil 



ti7S 



867 



31 S 



74 



19 



m m 




rroper Mmf 


VKM Mt vrmmr 


Of i 


5«-S^ 


t9 


36 


43 


3a 


6-t>^'9 


46 


6t 


26 


9 


7-0-7-9 


"4 


64 


23 


IS 


Sx>-S-4 


179 


69 


19 


9 


8-5-S-9 


44" 


77 


18 


4 


90- 


378 


So 


»5 


5 




Stam—CenUHHiat Prtfer Moliomt in 


Ord, 


UmlUof R.A. 

h h 
0- 3 


TMal 

KiMbarol 

SIUI. 

149 


tr-s* 

*7 


38 


5 


3-6 


I^ 


77 


16 


7 


6- 9 


137 


80 


13 


7 


9-12 


170 


70 


33 


5 


lS-15 


17* 


71 


ao 


S 


15-18 


140 


75 


<9 


4 


iS-zi 


147 


83 


<S 


3 


21- 


136 


74 


11 


13 



The mean discordance nf a determination of proper m. 
{rom Groombridgi- aud Carrington is +'010 in N.P.R 
+ '•011 in R.A., using those «ut9 only wliich have litile oi 
ajstematir emir vhich would f^ve a probable error for a r^* 
centennial proper motion of t±''3 a! thv effect of ( 
error. 



Dec 1906. Mr WitcJieil, Temporaiy £nors 0/ Division. 149 



'On the Afcidenial Prodvetion of Teniporari/ E'rron of Division on 
a Gradtiaietl Circle. By W. M. Witchuj'l. 

{GommwHicaUd bjf the Astrvnamtr Royal. ) 

During an examination, undertaken recently, of the micrometer 
I screws of the Lircenwich Meridian Circle re«ding mtcroAcopes, a 
soggestive discovery waa made. 

Six obserrationB of "runs" hud bean taken over each of tliroe 
consecutive intervals of 5', and thutie agretMl among themselves 
quite normally so long as the samp interviil was under coriBidera- 
tioD ; but when the resultii from the diflerent intervals wore com- 
pared a discordance much beyond the probable accidental error 
of observation appeared between the valuee obtained at pointer 
reading 89* 35-40', and those at 89* 40' -45'. 

As will he seen from the following figures, the diacordance 
amounted to o''oi4 or o'''84, and an atiempt to trace its origin wax 
necessary. 

Pa2tu of 5' <tf Cirtls in ' ' itetm .Vienmiler. " 





Polo tor 


89* jj' to 89" 

r 


40'- 


Folatcr B9' 40' 10 89' 45'. 

r 


Sftt I . 




4-903 




4893 


.. a • 




•91 J 




•89. 


M 3 - 




•908 




•897 


M 4 • 




•907 




^ 


.. S ■ 




■904 




•m 


.. 6 . 




•90S 




-891 



4*907 



4-893 



DifiSercQce : 0''Y}14 

An accidentally large deviation from the mean division error 
at thix part of the circle was at first au8p6<:ted. A searcti for others 
of like magnitude in the neigh bo urhooti, however, pnxluced negative 
results, lint when these ob«ervatinn& (which conhisted of three 
Beta of runs over each 5* interval from i«iiiter reading 88' 20' to 
89' 20') were amnged so aa to exhibit the values from the six 
micrometers individually, and M-ere compared with Lie former 
Bvries similarly armugodr it M-&a at once seen that the discordance 
took its origin in a large apparent error vif the patticular graduation 
viewed by microscope D when the pointer roiids 89' 40'. The 
ligurea follow. They were considered to give strong evidence of 
an error amounting to o''03 of micrometer, or I'S in this gradua- 
t' niuch as the mean screw meaeuienient^ of the two adjacent 

lU'Peared to be too lai^e and ti>o amall respectively by 
quantity. 



1 50 Mr WiUhtU, Temporary Err&n 0/ Divmon. LXVii. 3, 

Mefuurtmenl of 5' tnUnmt, 89* 35'-^* 40' poittw noAimg, 




„ 6 



4-887 
•915 

«W 
•»97 
•S96 
•891 



4*931 

'937 
■917 

•9*3 
■913 
•924 



Mwi 



4 91 4 



4-915 



4-898 4*92« 



4^909 

'9'4 

^18 

■910 

-906 

•901 

4*910 



4'S74 
•891 



Corresponding nifans of 36 other sets, viz. 3 otbf each 5' 
interval from 88" 20' U> 89' 20" ; — 

4^923 ^-918 4'-890 4"90i 4'-9l6 4"S84 
Mmmmmmi ^ 5' iwUnat, 89* 40'-*9' 45' roi-^tr naHinf. 



MiHwimii. 


i. 


B 


c 


D 


B 


V 




r 


I 


r 


r 


( 


r 


8fll] . . 


4*9'* 


4 '9*1 


4*871 


4-868 


4-904 


4-8fo 




•913 


'9to 


•869 


•867 


>>5 


«$ 




•917 


•89a 


•ast 


■873 


-916 


y»» 




-910 


•899 


-889 


•S90 


•90» 


•STfr 




•S96 


'916 


•S68 


■87s 


-911 


-•90 




935 


■908 


•89« 


854 


■90s 


««J 


Man . 


4*913 


41908 


4'878 


4-871 


4^907 


4«J 



Nov in the winter montha it haa been oustoni*ry to protect tfatr 
oircle from tArnish hy applying tu it a thin film of Tast-line, which, 
howaver, gradually accnitmlatea tmall particles of dost aod ts 
renored from time tu tinitf. 

Before proceeding to a syatAiualic examination of the circle for 
poiiihle errors of liko Ditturs in other graduatioos, the part under 
actual suftpicion nsA wiped clean ; when it was found that the sup- 
posed error of nearly a in the diviaion in <|uestion had abaolutelj 
aiaappeared, preoumahly wttli the dusty vuselme. 

It should he stated here thai the micrDsco|iw were in good 
focus and adjustment. 

Other dirisioDs being titnilarly expsrtmented upon gave m 
difference, before and after, at all comparable with the foregoiiiK^ 
•loept in one case (the fl)iures for whivh are ttu<>t«d below), eo that 
the Uahility to error intruduced by this mrilKiJ of preserving the 
otrcia is probably lx>th slight and (-itfuaJ. At the same time It ta 
distinctly real, and may be the i-xptiuiatiun of discordanoas which 
cannot be asoibed with certainty to other agencies. 



d 



Dec 1906. 



Obaervaiions of Minor Planets. 



I5» 



The following arc micrometer rendinga for ten bisections of the 
diyisioti under microitcope K (pointer reading 164* 4.5') before and 
wiping; off the vaftelint^' — 



Outatt. 


AfUr. 


t 


r r 


60S -611 


■633 '618 


•613 -612 


'627 '630 


■603 -604 


'639 '604 


•589 593 


•620 '633 


■603 '590 


•632 '624 



Mcui "603 Mi^ou '-625 

DttTerence: f'O23=i''40 

Ab a coDsequence of theeo reveUtious, the cWiiing of the 
circle, which hitherto lias naturally been avoided aa much as 
pOMible for fear of iDJuring tlie gmduatioiiR, v\tl be carried out 
more frequently. 



Obaervatiotts of Minor Pianeta from Photoyrajiim taken with the 
30-tncA Rejie^or of the Thmnpvon E<]uat<mai at the Royal 
Ohaervaiory, Oreentoicfi, during the year 1903. 

(Cmnnmrtieainl J/y l/it Astrowmfr Ro\i<i!.) 

The foUowing positions of minor phiiiete were ohtainBd from 
photographs taken with the 3o-inch ReEector during the jear 

1903- 

The plates were measured with the a.strugmphic micrometei*. 
Four reference aian were, as a rule, measured with the planet, 
their positions ))eing derived when pu8eihl(> from the Catalogues of 
the Astronomische GesellBchaft. 

The positions giren are not corrected for Parallax. 

log Parallax Correction = log I*arallax Factor -log A. 

Tlie anonymous planet was found on the aauie plate s« (407) 
Anurhne. 



DMSMidG.M.T 
1903- 


Ai>|»rciit K.A. 


Apparant I^ec. 


Log. pAHjlax factor. 

R.A. Det. 


« ■» 


b V ■ 


li m « 


. . . 






i 




(358) Tyche. 






Mar 35 


10 4t 39 


14 3S 6-48 


-7 40 SS'i 


4-8'33I 


+ 0-876 


26 


9 55 4t 


14 37 35 "65 

C6S) 


- 7 34 56*3 
Leto. 


+8-669 


+0*876 


May 29 


11 3$ 13 


15 13 4S'l4 


-3043 7'i 


+8723 


+0^1 


JtUll 3 


10 46 9 


15 10 |8'77 


- 20 38 34'5 


+8-463 


+ 0'92T 


3 


w 39 3 


15 9 28*86 


- 30 37 15-3 


+ 7*931 


+ 0-933 


4 


10 4 IS 


IS 8 40-18 


-2036 7'5 


-%-af:^ 


■vo-^*\ 



H 153 


C 


wHBBn 0/ Mirutr PiatuU. 


Lxra. 3, ^M 


^H iMt mod O.U.T. 


Api/umK B-A. Appsnat the. 


I10C.IVSIIU ractdr. ^H 


^^^^ 


h ■ « 


b ■ • ... 

(17) Thetis. 




H 


^V >i»r 39 


II jS It 


16 S9 51*84 ~ 14 II 6-9 


- 8773 


+0-901 ^H 


^H Jaii« 


tl 18 49 


16 56 13-69 - 14 >< 50*4 


-8-961 


+0-900 ^H 


^^^B 


11 11 36 


16 55 |6'89 - 14 i» 157 


8*983 


+0-900 ^1 


^^^B 


II 47 W 


16 34 iS-99 - U 13 455 


-8473 


-t-O-90t3 ^1 


^^^^H 


" S S7 


16 38 3083 - 14 38 548 
(511) DftTbU. 


+ 8*664 


+0904 ^M 


^ June > 


If 4S 14 


16 49 57*8 -9 13 4*5 


-8*511 


+0883 ^u 


^^^ 


13 9 3S 


16 49 101 2 -913 46*3 


'■7*9<i9 


^o-SS3 " 


^^^H 


II 37 1 


t6 48 34'63 -9 '4 J0*3 

1304) OlRfc 


-S736 


'O-S83 


^^^^^ Jbd« 3 


tl 43 3 


IS 39 iO'i4 -*>5 17 30'4 


+ 8*960 


-^0779 H 


^^^ft 


10 28 43 


15 38 33'8i -fS 17 39*8 
(434) Hanjiuk. 


-8-349 


+0778 ^M 


^^r jhm 3 


'3 33 56 


16 t6 35*39 +33 39 49-8 


♦ 8-935 


^H 


^^^K 


»o 57 43 


16 14 3650 +23 36 36-4 


-S-6S4 


■+0*636 ^H 


^^^H 


10 35 59 


16 57'07 +31 55 8*3 


-S779 


+0*636 ^H 


^^^K 


10 u 53 


i5 59 S7'33 +»' ¥> 3** 
(433) Vythia. 


+ 8711 


+0*640 ^H 


^H Jaiu: 22 


II i7 43 


16 53 3^91 -19 46 40*1 


+ 8760 


+0-919 ^1 


H 


10 36 4S 


■6 47 5^"^ -so 26 1*9 


+ 8-077 


+0*931 ^1 


H July 1 


>o J6 53 


16 44 39-33 '*> 57 3<"9 
(4OS) ThU 


+ 8-647 


+0-933 ^M 


^H Jtuuu 


II S4 SO 


•7 33 0-93 - 19 »9 SOT> 


+ 8733 


'*>o*9iS ^^ 


1 


II 43 34 


17 iS 40*46 - tS 53 17-8 


+ 8878 


* 0-915 1 


H Jb>T > 


It S 3 


17 15 36-33 - 18 36 19-0 
(370) Anklilu. 


+ B-614 


fl 


^M AOff. 4 


'1 57 $» 


*o 33 35-63 - IS 13 sj-6 


+ 8-616 


+0-906 ^H 


^1 


10 38 14 


30 31 33'44 - 15 16 ;-6 


* 8-915 


+ o*gcH ^H 


^H 


10 >9 57 


» 17 jw - 15 27 34*4 


-8-749 


+ 0-906 ^H 


^■^ 


yjtf-M 


» »4 JSS* -15 34 7-1 


-8-934 


+0-905 ^M 



Dec 1906. Ohervatiom of Minor Planets. 


153 H 




ApiitnDt E.ii. AppMVBt D«c. 
(57) Mnemoayue. 


Log. PAnllax Faclur. ^^| 
£.X. Dm. ^H 


d 

Aog, 4 


b m I 
" 39 55 


h m a c , It 
19 39 a7"24 +0 10 56-1 


+ 8-899 


^M 


S 


9 44 42 


19 38 50-55 +0 6 49-3 


-8-984 


^^H 


6 


10 9 35 


19 5$ 10*50 +0 2 S'5 


-8-694 


+0-836 ^^^H 


7 


10 644 


19 37 3<'W -« 2 336 


- 8-M5 


-fo-836 ^^^H 


10 


10 9 34 


ig 35 40'J0 -0 17 17^ 


-8-317 


+0-83S ^H 


13 


9 2S 56 


19 33 56 "84 -03343-3 

047) Protogema. 


-8-803 


+ a-8j9 ^H 


Aug. 5 


tt a 19 


21 34 0*63 - 13 32 43*0 


-9 "23 


+0-892 ^^^H 


13 


u 7 46 


21 17 5219 - t* 59 26*6 


-8-865 


+0-S97 ^H 


2J 


11 14 t 


21 II 503 -13 29 539 
(407) Arachne. 


+ 7'693 


+0-900 ^H 


Aug. S 


II 25 49 


31 44 50-01 -7 53 4-4 


-9127 


+0-875 ^M 


6 


10 59 as 


21 43 58-35 -7 53 SO'5 


- 9-221 


^^B 


31 


n 35 II 


31 21 21-39 ~8 33 47*6 


+ 8-808 


+0-&S0 ^^^H 


^ Sept 1 


9 59 38 


21 20 3637 -8 35 37*0 

(.\noaytnouii, ) 


- 8*819 


+0'8So ^^^^1 


1 Aug. 6 


10 59 25 


21-40 47'S3 -7 30 8-6 


-9-209 


^^M 


■ '' 


II 35 11 


31 30 30-19 -8 17 4*9 


+ 8-S19 


+0-879 ^H 


■ Sept. 1 


9 59 38 


at 19 5208 -8 19 35 '8 
(324) Bftmbei^iiL 


-8-819 


^H 


1 Aug- 31 


II 5' 34 


22 3 40-60 - 9 43 8'3 


+ 8-589 


+0-8S5 ^M 


H Sept. 1 


10 17 35 


33 2 4334 -9 37 21-3 


-9-023 


+0-8S3 ^1 


■ ' 


9 40 II 


ai 56 4523 -S 59 412 


-9-071 


+0-8S0 ^M 


■ ' 


10 u 59 


21 54 53-38 -8 46 383 


-8-699 


+0-881 ^M 


L 


10 33 9 


21 53 7S3 -8 33 31-1 
(333) bodcuia. 


- 7*509 


+0-SS1 ^H 




10 5S 46 


32 33 49-07 -10 51 33*3 

(184} Dejop«ji. 


-8-387 


0-S90 ^^^^H 


^^ Ang.31 


12 54 «7 


22 41 3-51 8 13 1-4 
(5'4) "903- M. H. 


+ 8-!i95 


^M 


1^ Aug. ji 


13 3047 


23 54 43'86 -0 54 48-9 
(5»3) '903. [*■ V. 


+ S-991 


+0-S41 ^^^^1 


Aiis.31 


13 30 27 


23 II J4-S3 +0 28 507 


-SJ79 


+ 0-*^T, ^M 




154 



Mr A. FowUr^ Enhaneeti Lint* of Iron. LXtti. 3^ 



Bidumad Lim$ cf Iron *» Me Jiiffion F to O. Bj A. Kowlcr. 




Id view of the dow gonerally reeuj;nitf*^d importance of ea 
lines in (he inierpreUtion of soUr ami sUlliir ii]>cctr«f it it 
thAt the uccom|>auying nb^eriiitionM of the enhAiioeJ Iidm of i 
which occur in the Ie« refnngib]!) porta of the spectmin maj b« 
Qseful to other workow. 

The line« buve boeti observed and photognphed uodor wiotu 
oonditioiu: in the spark, in the arc at reduced preasnre, in the an 
in bydroRen, and on the |>oiitivt) polo of an ordinary conlinnoo*- 
currunt arc in air at atmoapheric pr«B8ure, metallic oluctrodM buiug 
usrd throaghont There is a distinct gain in imxliicin^ the Mam 
withoat the use of a spark in n few casea, iuasmuch a« ther« k M 
air spectrnm to interfere with their detection. 

Tbo occurtvnce of the enhanced linos on the potitiT* piJe of th» 
MO afTorda a particularly convouiont mode of iJentifyiag theni, 
except towards the nd, where the continuous ft|>6Ctrtim tends to 
mask the fainter ImM. When tht* bright s|K)t on the positive [fola 
is carefully adjuslod on the slit, the lines in questiun are obasrvMl 
as very »liurt line^. quite dtfTen-nt in appvoratice from the are Um^ 
which are also present and provide a convenient reft- rence spectrom ; 
unlike the enhanced line^ the arc lines sre either weakened or 
uneliaii^ed on the |>ositivt! [>olu. A similar appearance is obawved 
on thu negative pule, but tho enhanced lines are not so bright. In 
these experiments the current luis ranged from ix Uj o'4 ampins, 
on iio-Tolt circuit, with an approximately constant poteatial 
difference of 40 voltt between the electrodes, and the intonsitifla of 
ths anhanoed lines have not boon found to be matoriallj changod 
as compared with the arc lirxes observed at the same time. Even 
with 0*4 amp^rest the arc burning oontionously, all the arc Uiiee 
remained viaibte whan the proper part of the image was broui^t qd 
the slit, and the enfamnoed linea were alill very distinct m the 
iinmediat« nei^hbourtiood of the polee. 

riiis result u somewhat different from tluit nlitaJnrd by [lart- 
maun with ms^nMdum poles, in which caae the cnliancwtl liitc 4481 
is greatly »tr(>n^'theni>d as the currant is reduced. It diSem also 
from Prof. Halo's rvoent observotiutii of the iron i^peciram^* in 
which a s-amp^ro arc was found to give n spcctnim closely 
approximating to that of the anter tlame of an ordinary are with 

f;retter onmnt^ tbongh no material change was obeerved in posaing 
rom 30 to 15 amp^rea. It may be that the difference is jiartly 
due to the use of raetallio electrodes in my oxperimviila, while 
Prof, liolo a{ipetm to have used tim melal on nu-^xin p«tle« ; ondar 
the latter conditions I hove obtained similar rtnutta with tW 
3-amp^ie arc, but only when the quantity of iron on the polea wm 
small At ail events, when ntetoUio polee are mod, redaetf«& of 
current strength doee not *ppMr to be aeooopanied b; a radoottoa 
of temperature sufficient to prod ace any notable diffarenoaa in 

' ^i^njiSy. •/memo/, to), xxlv. p, sot. 



in^^ 



Dec. 1906, 



in the Region F to C 



155 



spectrum, if ('orresi>onding parts of the ore be observed in each 
caee. InJfced, this observation acconlft well with Prof. J. J, 
Thui)L»tjn'» remark * that in the arc " the temperature of the 
crater of the positive terminal remains conHtant even when the 
curruut varies." 

It shouhl bu romarke<l, however, that the simUarity of the 
phenomena in the a-ampi&re iron arc with those observed when the 
current strength ut greater doe^ not iu the least invalidate Prof. 
Hale's conctuHiun as to the probable low temperature of 8uu>8pots. 
A» in my own discussion of this point, t Prof. HbIb's nrsult ulti- 
mately depends upon a comparison of spot spectra with theapectrum 
of the arc-A(ime. 

The wave-leagtha of all the Hues given iu the table have beeo 
deteruiined fr(im a new series of photogmphs in which the linear 
dispersion from C to K is 24 cm. The results have differed so 
slightly (raivtly more than 0*02) from solar lines of a[it)ri>priate 
intensity tabulated by Rowland that there can be no doubt as to 
their identity, and to avoid any possible confusion, Rowland's 
wave-lengths have been ailopted. Tliis procedure is, in fact, 
jufltiried by l^ockyer and Baxandall's demonstration X ^^ '■^^ presence 
of enhanced lines of iron in the more refrangible parts of the solar 
spectrum. 

The represcultttion of the additional lines with proper iuteasities 
in the Fraunhofer spectrum, together with their special behaviour 
in the chromosphere and spotii, § is valnablo confirmation of their 
classification as enhanceil lines. A few Hnes, ntitably two at wave* 
lengths 53&o'5o and 510095 which appear in some of the spectra, 
have not beeo includer3 In the table because tliey failed to satisfy 
the^e conditions, although the probable impurity produciti);; them 
han not yet been traced. That Auch lines were due to some sub- 
stance other than iron was further suf^'ested by their variable 
inteoMtiea with respect to undoubted enhanced lines. Prof. Hale 
has met with a nomewhut similar cm(^ in a supposed enhanced line 
of iron at 52i8'37, of which he says that " the enhancement of this 
line may vary." Here, however, there can be no hesitation in attri- 
buting the Hue to copper, which is a very common impurity in iron. 

There i^, in fact, uo reason to suppuso that the intensities of 
the enhanced [ine.s are appreciably diffiirent relatively to each other 
under any of the conditions of cxiKriment which have heoo 
mentioned, though their intensities, as compared with the arc lines, 
are nut the same in all cases. The euhancemuut is must marked 
'in the sfiurk spectrum. Estimates of the relative iuteDsitien are 
given in the table. 

For the sake of completeness, the table also shows the be- 
-of the litiBs iu the chromosphere and sunspots, Y, H, M, 
nectively indicating Young, Hale, Mitchell, and Fowler. 




■kargt ^ EUctrirUy tAraugh Gatft (1903), p. 417. 
'«^ Sotttr Vyi.\*n\, Tol. i. p. 22S(i9o6). 
ml. Uciiv, p. 335 (1904). 
mL Ixri. p. 361 ( 1906). 



156 Enhanced Lines 0/ Iron m tht Kegion, FtoC, utvi 



CabUMd tm. I> Kowlud. 



49*411* 9 

50I8-63* 9 
S169 u* 10 

$19774+ 4 

5»W79t 4 

Sa64-9« I 

531679" 9 

5363-06T 5 

5535^06* 4 

6138-^ 3 

634777 3 

64i7t3 a 

64S6'6ot 6 



Ft) 



r* 



ref 



B«>bKvlo>ii In Sw)> 

WMkrned H. F 
.. H. ¥ 

H. U. F 
, H. M. K 

H. M. F 
„ n. F 

Not rlMrly fttfectad 

U. F 
W«.kcnrd Y. H. F 
,. Y, F 



Utaoilljrla 
nhtnHKNplMr*. 



V 
10 

tS 

as 

10 
10 

3 
10 

3-ao 

a 

S-io 

13 

3 
4 



M 

>5 

10 

a$ 
15 

'5 

7 
S 

30 

10 

8 
13 



as 
»S 

40 
as 
»5 
'5 
35 

45 

15 

30 
3S 

'5 

30 



Conponnil Um is 

4.. ;6*»4. 76-17. 



Ravlaod'i 
too liigb. 



-4 



in AfHrk. 



ObMTTWl tlio 

•pukbr MiulwU. 



... 3 „ n*r j-io 5 20 

It will be wen Uial the roprwentAtion of the eohanced Iimh 
Id the loliLr i[«ctniai, aod in the Kpectnim of tht* chroiuot|>hcf« 
uid son-cpota, w quite cuuniittvui thruughuul. Aji in thu eu» <A 
Lockyw Aud Uax&udall'i investi^atinii of thu utorc nfnuifrifalB 
IMrto of the •pectrum, ongios are iiov provided for svvertU Udm 
nnidantified or doobtfully idetititieil by Itawlaod, the rouou being 
that he did not ordiuaril)- ohtain the weaker enbtDCttd tinea m hia 
pbotographii, and probably attributed their oocaiuoaal appearanct 
to inipuritiea. 

There is abondaot evidence that all the enhanced linee of 
iraoin the region F to C are weakened in th« spectra of iian-epoti, 
and the work at Mount 'Wilnun baa already ahown that the woe 
is true of many of the linc« of thia clan in the blui' and violeL 

All the lines in qaettiou arc alao promineut in the apectram 
of the chromosphere , and, aocording to ray provioiM obeervationl^ 
are of the high-level tyiie, with the poeeible exception of 64177, 
which is not yet included in my tiat, but is given by Young. 

It is euAiciently clear, therefore, that the enbancad linM 
oODititute a special systrm of linm which vary together both ta 
labomtory experiments and in the various parts of the son where 
tbey are observed. 

NUe. — It may be mentioned that, while generally ooDfiming 
Lockyer's tiat of etkbanced lines of iron in the more relrmngible 
parts of the ■i>ectTiim, the special photogrmphs of the arc reveal an 
additional line of coiisideraMu intensity at 4416*98, which is 
masked by an air line in the spark. This ltnt> also is wemkeoad io 
th« sun-spot spectrum. 

* Prwiooaly neordsit by Uekyv. /W. 5*/. Phyt. OU,, 1906, etc 

f „ „ Antbor, UotUMjf Kotieu, vol, li*i. p. 364, 1906^ 



I 



i 



Dec. 1906. Mr A. FowUr, Silicon in the Ckromwphtre. \ 57 



Nate on Silicon in the Ohnmoiphere. By A. Fowler. 

Pending a more complete investigatioQ of the spectruiu of 
silicon m relation to the chromofl[fher«> and Sun-flpobi, it may be of 
interest tu dniw attention to the identification of two strong red 
lines of thie clement with wclUmaTkeil chromospheric linos. The 
lines in question have been previously obeerved in the spark 
apectrum by Salet (AA. 6341, 6366), by the Count de Gramont 
(AA 6342, 637c], and more recently by Lunt, who gives the approxi- 
mate wave-lengths 6346'9 and 6371*2.* 

A careful re-<leternitnation of the positions of these lines, from 
pbotograpbn giviti;^ a linear dispersion of 10 tenth-metres to the 
millimetre in this part uf the spectrum, leaves nu douht as to their 
coincidence with the proviuuely unidentiSed bigh-lovtil cbromo- 
apberic lines at 6347'3i and 637i'57. ITie mor« refrangible of 
the two line* id the stronger, in the pro|>ortioii uf about 10 to 6, 
and their iutensitiei! in the cliromosphere, according to my own 
obuarvations,! are 25 and 15 respectively. Both lines occur iu the 
Fraunhofer spectrum, with intwistties and charncter* aN and iXdt 
reiipectively, and Rowland assigns tbp latter to iron, while leaving 
the other unidentitied. Kayser and Kunge also give a faint line at 
637i'6o in the arc spectrum of iron, but it d^ies not apf>ear on my 
pbutogmphs of the iron spectrum, except when the presence of 
silicon is indicated by the other line al 6347'3i. In any case, if 
there be an iron line at 6371*57, it is not an enhanced line, and is 
not of snfKcient intensity in the arc to account entirely either for 
the Fraunhofer ar cbromospheric line at the same wave-length, 
which must uccor<lingly b(< attributed chiefly to siHcoD. 

In Sun-spots, according to the observations of Mitchell I aud 
myself, the two lines are almost obliterated, so that there is a 
complete agreement of behaviour and intensities throughout. 

The relationships of the difTerent families of Hilicun lines have 
not yet been fully worked out, but it is probable that the two red 
lines, like so many of the other high-level chromospheric lines 
which are weakened in spots, belong to the enhanced line class. 
Like the enhanced lines uf irun, they appear close to the positive 
pole when a little ulica is introduced into the iron arc, nod the 
wave-lengths have been determined by reference to adjacent iron 
lines which occur with the silicon lines under these oonditions. 
In hi^ recent discussion of the violet part of the Bash spectram 
Pr<.i:' concluded tliat there was "a fair degree of pro* 

'^^* tie exifltenoe of silicon in the chromosphere," and all 

removed by the identification of the red lines. 

"apf OAMTTotory, vol. x., Psrt IL. p, i8b {1906J, 
. vol. Ixri. p. 365(1906). 
- vol. sxiT. ji. 92 (1906). 
' A, p. 440 {ISO*)- 



IS8 



MtB.F. 



LXTtL 3. 



Nuttt on tome Spedroteoptc Obtervaiioru of the Sun, 
By H. F. Niwall, M.A., F.R.a 

Speeuoacopio ob«ervationB of the ;Suii htve been ciim«d 
during the pMt year at Cambriilge. In the euli«r part of tlii> 
year Uie ohMn*ationa vero niado tvitb the 35-inch eqiuitorial (tlu 
Nswall telescu(je), to whiub a diffractiuu-^'ratiDg spectnwcops wu 
ftttacbed. In tho later montha a lixed horizontal t«1«acope ma 
improvitod, light being dir«ct«d into it by nifans of a coloetat 
and an aaxiliary mirror; and a much mora powerful grating 
•[•ectroscDpe was used. It wil] be convenient to refer to tlieee two 
equipruents as tho O(|ualorial and the horicontal. 

The gpnf^ra] programme wan to tejit by preliminary obaom- 
tiomi, whpthor thp conditions of atmoepherc over the fint platoa 
of Cambridgeshire would justify a ipecial outfit which anould 
unable u» to take some active part in volar work. It seemed 
thnt the atuily of sun-»ftot npectni would he a tittiuf^ nue for 
making the trioU. For, in thiA work, not only i« a fairly dear 
atmoaphere desirable, Huch ax will not proTent the detection oi 
faint eharact«mtic detail in tho suu-«iiot «pwtra by tho orcr 
powering effect of integrated aniklight scattered by inlvrveniog 
boae ; bat aUo a steady atmosphere is needed, tuch aa will not 
give riite to jumping images and the blurring effacta due to the 
•pread of circumiienumbral light over the umbra in oonaoqucaca (A 
atmospheric tremor. 

Accordingly a programme was adopted to iitelade spectroscopiQ 
obserrationa of nun-spots and other details on the solar surface, 
but not ofaaerTaiions of promiuencea at the limb. 

Hy idaa was that it would bo best, in the first instance, to 
ntiliae the equatorial equipment to gain pnotical ideas o( tb« 
difAcultits to be met, and the advantages to be gained, in direct 
|>ointing at tbu Suu with a t«leiKope wboae ohjoct-dlojot would in 
general be ntiuut 30 ft«t above the grouml. And tlirti, if the 
obMrrstJons proved to be generally encouraging as regards atmo- 
ipfaeric conditions, a horizootal equipment was to be Iriwl, with the 
beam about 6 feet above the ground. 

The result of these trials has been completely eatis&ctonr and 
decisive. The observutioos with the equatorial e<jutpmcut ibovred 
that good conditions of observing weie available in the early 
morning between 6 and 9 a.m. 

The obaervitions willi tlie hnrixontal equipment sliowed that 
UiBM conditions arv not seriously impaired by bringing the beam 
nearer lo the ground ; nny deleriurvtton arising from greater 
proximi^ to the ground is probsbly more than balanced by the 
vaatJy freer eirealation of air in the path of the optical beam in 
the open doma u oppoaed to the cImho.) tube of tho equatorial. 
Tbe conveniences of working with the horisoatal equipment — on 
a fixed floor, with fixed apparalna, with eya-piaoa in constant and 
aporaoJMit /xisition, with all the parte eaauy acoeaaihle, and mnat of 



4 



4 



4 



Dec. 1906. Sptcti-oscopie Observations 0/ the Sun. 



159 



all, with the power to uae very pon-erCuI spectroscopes— can hardl; 
be overatautd. 

TJie hAjuaiorial JCtjuipmeni. — For these solar observations the 
Bpeinire nf the s5-inch object-glass wns reduced to la inches, and 
the object-glass was usually between 35 and 30 feet above the ground. 

A powerful gratiuj^ spectroscope was attacheil to the equatorial 
in the autumn of 1905. A 8[««ial inountiug of a planw grating 
ha<i bpeai constructed t« replace the prism-head of the fo^^priBm 
spectrograph which has been used in stellar work (jI/.A"., btv,, 
Flatesi iSr 19). The beam which issues from the collimator is 



SLIT^ / 



PRISM \~ 




■ '- -1...^:: f ^^^^■'""^G 



CAMERA 



Fio. I. 



deflected througli 8 right tingle by a prism fixed in the grating- 
head ; the deflecte<l beam falls on the grating, and the camera 
is fixed so as to reci^ive u beum emergent at an anglu of 30* to the 
incident beam, and at an angle of lao' to the &xh of the equatorial 
and true collimator. Different urdont of spectrum are brought 
inlii the field of view by turning the grating, which is geometrically 
mounted in a <r-ast-iron frame capable of rotation about an axis 
coincident with the middle ruling of the grating. 

The grating is one ruled by Rtmlaiid : the ruled surface has 
an area 5^ inches x 2 inches on speculum metal, and the lines are 
ruled 14,438 to Uii! inch. 

The grating and collimator and camera are of such dimensions 

o transmit a 2-inch beam. The ratio a'/ is -^ for both 

und camera, the etTcctive aperture of the diapbragmed 

the equatorial is only A. but the slit of the sincttiv 




l6o Mr B. F. Newali^ IMes on some IXVJL 2, 

scope IB adjosteil to «ncb narrovness that th« diffractiona] ipread tf 
the beam in the collimator UlU the lenit latenlly, anil crouaequectiT 
the rettolving power of the gifting \a a 2-iDch beam is utiliaablt 

The iBpflctrum of the se^inii onler has genemlly bueo tu»l, 
aad of the two spectra of that order, that iu which the disperiiaa 
and magtiiCcatioD arc greiitvr Ii&h been cbosen. The ^crating kv 
been udjusteit in ita frame in such a way that this a|>ecial spectro 
shall be the brighteat available. 

In the winter months work with the equatorial was aomciiiM 
interrupted by conden&ation of mointiirn on that surface of tk 
dbject-glasa which ia nearest to the obyerver. Openin|i;B wen ctf 
through the tubi; vf the uquiitorinl clothe to the object-glass; uA 
ventilation, conirolled by shutters of the "hit-and-miBs" tfpc^ 
promotwl. ■ The! tTouhtea of condensation did not recur. 

The metal diaphragm, used in the first instance to cut dovt 
the a|jertiire of the objecl-glasit tu iz inches, was found to tautt 
great disturbance of the intake on the nlit. When this aalj 
heated dinjihragm wtut Ahielclud by white cardboard and n 
mented by a shcirt tul>e (12 inches in diameter) made of tin- 
and projecting about 12 inclies outwards towanls the Su 
air curronta were iu piirt mitigated and in reuidut; diverted 
the path of the beam used in iihtiervntion. 

One of thi5 4-inoh tinders attached to the equatorial was tuo- 
vided with a projection s'jreeii, and was used in setting any 
desired spot into the lield ul view of the guiding eye-piec« of the 
spactroacopc. 

It was found of groat convenience to get a qttick roeofd fi 
the spots visible on the disc, lm,'ether with means of orientacun. 
Photographic "printing-out" paper wan laid on the pttgectioa 
screen, and half-a-mlnute's exposure to the Sun's image was enouh 
to give a negative print of the requisite density. Orientation vm 
given by the properly adjuittud crot^-wires in the focal plane >4 
the finder ; they appear as white lines on the negative print of 
the Sun*H disc. 

The ffor'izantal Eqaipment. — The object-glaws of the 25<tDei 
equatorial was dtsiiuuinlvd, and R.xed in a stout wooden frao*. 
with its optical axis horizontal at a height of about 6 feet abon 
the ground. The apenuro was reduced to 13 inchcis, and Mini- 
times to 6 inches. A 16-inch ccelostat was set up in a small 
building to the south of the ilomo of the Newall telescope. Bf 
an auxiliary mirror {also [6 inches) the beam from the c<¥-J<«ial 
was reflected northwards through an opening made id the dome, 
and therein the beam ptifised through the objecUglaas, which ww 
set with its axis pointing north wardin along 11 linu which lay « tW 
feet to the west of the pillar of the temporarily dieusod en» "' 
The ohject-glasfi was placed within a few feet of the 
of the dome ; and as the dome is 40 feet in diamete*- 
focal length of the object-glass is 29 feiit, there wa* 
to set up a large spuctro8coj>e iu the uorthern pai 
with the slit in the focal plane of the objecit-glass. 





)ec 1906. Spedroscopic Observatiora of the Sun. 



161 



The spectroscope used was the fine instrument built by Messrs 
[Cookeof York, for the late Professor Piaui Smyth ; it lias been put ti 
'the dieposal of the Obeervatory by the Koyal Society. The leosee of 
the collimator and caniL>raarH4 incheR ici «Iiauieter. The focal lengtli 
[Of colliniati^r is 53 inches, and that of the simple camera is 67 tncbce ; 
Ia negative enlarging lens can be inserted in the camera, and it has 
\hwu used in inicb adjtutmeut &n to give on affective focal length of 
ia fcft 9 iuchea for tbe cameru. 

'I'he plane grating tised with this inctrument is one ruled by 
BowlanJ, and hiui a ruled niirface at 5 inchen by 3^ inches on 
speculum metal, and th<.> lines are ruled 14,438 to the ittch. The 
second order of spuctrum ■waa generally used. The slit was 
usually made narrow enough to give a diffraetional indicator Ibah 
than I on the 4-inch Ikdr of the collimator (J/.A^, Lxt. p. 61 1). 
Records of the poaitions and number of spots were printed photo- 
graphically a-s iu the case uf the eijuaCurtal equipment ; but in this 
ease the printing-out paper was held on the slit-plate in the focal 
plane of the object-glass, firienlation being recorded hj the shadow 
of 8 wire stretched in front of the photographic paper. 

The horizontal equipment was put together in a temporary 
manuer, but in building the cculostat houiie aud making the windo^ts 
in the wall of the dome, all airangoments were mnde in sucho way 
that, if the preliminary observations provod satisfactory, a permanent 
equipment could be installed, on the same general lines, but with 
tliis following iiiudiiI<.-atioa : — 

Permanent Horizontal Equipment m Proeets 0/ Oonstradion. 

The coeloslat house is to contain the cuelostat and auxiliary 
mirror aud an adjustable object-glass of aperture 12 inches and 
focal length about 6a fe«t. The focal plane of this horizontal 
telescope will lie in the North Annex, a convenient laboratory on 
the north side of the duiiie of the Newall telescope. The 8pectro> 
Bcopic and other apparatus for studying the imago of the Jiun will be 
entirely in the annex. The dome itself will be used simply as an 
optical gallery so far as the aolar equipment is concerned; the 
equatori&I will be thus completely available fur stellar 'work, 
uolmmpered by any »olar apparatus in the dome. 

For the oolar work, the beam from the ccelost«t to the annex 
will thus pajis through shady places well protecred from direct 
aolar radiation and from disturbance from detrimental air currents. 

The cost of (he t-quipincnt for solar observations, which repre- 
^aentft a new d'-parmre ai the Cambriiige Observatory, will be met 

aii app ropfiatioD from the Frank Mc('lean bequest. 



' C€m>iitiong bettneen 1905 Nov. 24 atui 1906 
■Stpt. 30 (310 days). 

lummarises tlie atatc of the sky for 
jtB that for at least 7 houfs id 



1 62 



Afr B. F. N^eioall, Motes on some 



LXVH. 







0*arcMt 


Hiiiiht. 


Suoatiln* 
bet«*e«n ClouiU. 


n«ie. 


ObMrttoc 


1905 


Nov. 


■ 5 


2 




... 


1 




Dm. 


22 


7 


2 


... 


6 


1906 


Jan. 


- U 


6 


10 


1 


8 




Fob, 


. 18 


2 


6 


2 


J 




lHu. 


. 33 


7 


2 




4 




Apr. 


■ <3 


9 


7 


1 


a 




M»y 


■ 2} 


4 


5 


1 


3 




Juno 


. u 


S 


8 


3 


4 




July 


. 16 


12 


1 


... 


9 




Aug. 


■ 13 


13 


2 


] 


»5 




fiepL 


■ IJ 


It 


4 


3 


S 


1 




>73 


7I 


45 


1 1 


S9 


1 




134 




1 


F 






No rMonl 


on 3 days. 




' 



Nearly all obaervors agree tbat the early hours of the luoroing 
are the most favoitrable for solar obserrationR. Experience saoD 
showed that Cambridgf was no exception to the general rule, and 
it is probably no exaggeration tu Huy that t\vu minutes' ubservationa 
between 6.0 and 9.0 a.m. reveal more than an hour's work ue&r mid* 
day. Nearly all the observations after May were made in the 
early hours. 



Observaiivm on the Nature and Auwunt of Skyalare. 

Sun-spota art; observed under trying conditions- We look ail 
Vhem through a bright sunlit veil in the Earth's atuiDsphere. If j 
the veil is illumined by the Sim to unch an extent that the veil 
is as bright as the umbra, thun it is to be ex[>ected tbat details in 
the spectrum of the umbra will only hv. discerned with difficulty. 

Everabed's experinii.!nts* led him to the viow thtit in the greea> 
and yellow port of the spectrum the brightrifwf? of the umbm was 
iiboiit ^'j[th of tbat of th« Sun's surface. AV. E. Wilson found t] 
that his measures with Boys' radio micrometer indicated a 



If we adopt Kvershad'e value as applicable to obnervntiona inl 
the visual part of tbe spectrum, we should expect tlmt charactccw] 
iatic details in the Bnn-«pot spectrum would be diflicnlt to discern,! 
if the brightnosa of the sky-glare were ij^th of that of Uie k>1i 
surface. 

Now this V4)il or eky-^lare is to be attributed to two main 
causafl: (t) scattering by fog or haze or air, (3) scattering by 
atmospheric tremor. The finit of these, acting atum:i, would 



t Obatnatmy (189S), ixi., 379. 



uld give «fl 



H)ec I 



1906. Speeiroacopie Obteroaiums of the Sun. 



163 



I 



I 

i 



zuilky sky in the uei^bbourhood of the Sun in the sky ; and the 
milkiness would no', be vei-y different over the centre of the Sun's 
disc from wli&t it is at, let us «ay, 5' or 10' outride tfie Sun's limb. 
On the other hand, sotttering by atmospheric tremor, though nearly 
uniform over the Sun's dbtc, would fall away very rapidly outside 
the Suu'a limb, and wouM probably not be very marked at 20' or 
30' from the limb ; it would be evidenced by the " boiling " of the 
limb and would be greater with largo objoet-g lasses thau with small. 

Some atterapta were made in the early part of the year nt 
Cambridge to get from a series of photugrapbs quantitative 
infoniiatinn as U> the brightue-ss of these compoueiita of sky- 
glare. We may express the brightness of the haze by h», h being 
the hsze coefHcient and n being the bnghtnefls of the Sun's surface 
reduced by absorption from its true value S as it would appear 
outside the EnrtVs atnioaphere. Similarly we may express the 
brightness of the veil spread by tremor by ig, whore t is the 
tremor coefficient. By spec^tnim phntngraphe which show a com- 
parison of the Sun's surface with the sky at 5' from the limb, and 
by spectrum pholoj^Taphs which show a comparison of the veil and 
umbra witli the sky, we get two eijualioiia which would give 
h and t, if we knew w/*- the ratio of the brightness of the umbra to 
that of the Sun's surface. 

If there werti no illumiued veil but only an absorbent atmo- 
sphere between the observer and the Sun, the ratio u/ir = K would 
be the same as U/S, the true ratio of umbra and Suu's surface seen 
from ontsidfl our atmonphctre. But the veil gives rit^e to an equation 
of the form (approximate) 

K -I- Aj* ■*• irf =« Aa 



R = ^ 

e 



'k-(h-^t) 



Where k is the observed ratio of umbra and Son't Burface, seen 
through the veil. [Evemhed measured k under presumably favour- 
— Able circuntstanccB, and found k= 3^^.] 

" The observations at Cambridge were directed to getting some idea 
of the order of magnitude of the qnantities R, A*, h, an^i (. The 
results hardly warrant more than hazanle-l opininnM that (I) R the 
true ratiu U/S is more usually nearly ^'q^, and in certain cases it is 
probably aa small a.i yIc i »i'l (^ * "^'th rei^'ard to the values of h and 
/. though we found tltat k ranged from -^^ to ^^, and that / might 
rise to as much as, i, without completely oblitifratinfr the most 
marked characteristic? of suD-spot spectra, quite usual values for 

n and t are ^rnr ^^^ thj- 

r It is evident that the nature of the case is not such aA to 
justify elaborate measuremonta. The estimates here given are 
based on comijarisons of density of deposit in photographs takeu 
with varied aud relatively a^usted exposures, under conditions 



k 



164 



Mr S. F. NeicuU, Notes on iome 



Lxm. 



n 



chosen for fair compariaon. I should add that the obMTvationi 
were carried out mninly in the winter and early siting, gsnerallj' 
on daj8 whcQ the tieeing wiu not good enough to encourage the 
search for special tletatl in the spectrum hut not bad enongh to 
obliterate it altogether. 

On'U point stands out Tery clearly, caniely, that since tht 
chancterietio detnila of suii-a|:iui spectra are discernible, even wlwii 
the veil of iotegrated sunlight is as uuch as perhaps a quarter of 
the brigbtnesH of tlie Sun'a surface, those delails must be verj 
marked. 

Another [loint which I would like to emphaHiae \» this: — 
The haze component i»f the vei] is probably liardly to be dis- 
tingiitiihtid spectroscopieally fwm true intogmtcd simlight^ except 
in the relative brighttie*? of widely separateii regions in tlie 
spMtrun:. The tremor component, on the other hand, i[it«gTatei 
the sualight only withiu. let us say, 30" of the point considered. 
Thus over tilt; uMibrn of a tipot the tremor component throws 1 
veil of illumination which cntnes only from the neighbourhood of 
the Rpot — that ift, from regions which are coinpanible with the 
large flocculi exhibited in Kale's Bpsctroheliograras, and which io 
other ]>art« of thojie notes I have veiitureil lo culL L-ircuuipenunibral 
regiouii, where the apectruttcopic phenomena certainly indicate 
spc'ciul dixturbed conditions of solar strata. It is obvious that 
the&e points have a Tory marked bearing upon the interpretation 
which roust be put upon bolometric observations of sun-epota. 



Differeaicet in the Wayt in whieh Lines are qfeded. 



Thfifie preHminary observations have le>i ma Btrongly to the via' 
that one of the moat promising lines of study must be that of Ui 
differences between the ways in which various lines are affected i 
or near sun-spots. 

My observationa corroborate in ver>' nuiny jwiutH those of ma 
obeervers a.s to the existence of lorn; lines, short linoe, wiuged 
etc, such as are epitomised in the drawings of characteristic 
given by W. M. Mitchell {Astrophys. Jour., xxii. p. 6, PI. IX 
by Fowler {Int. Sol. Heeearch, vol, i. p. 238, I^lato). 
dark Hues havu been seen in the spectrum of the uuibra, an 
hazy dark lines : some of the dark linei^ which are fairly alroni 
over the circumpenumbral regions have been seen nearly, if 
quite, obliterated over the umbra. But I incUut- to a^ree wi 
Professor Hale in requiring further evideucc before I am p 
to say that I have seen tines aotnally revenged into brightneaa 
the umbra. With raspact to the teidming of lint-s, I am in 
doubt ; it would appear iiidisputabiu that with certain insl 
coiiditiouii linea appear to be widened, but it seeniii to me t 
phcnomeoon diaappeari wheu spectroscopes of high powers arel 
I revert to this in the next section. 

My observations completely corroborate Professor Fowler'a to 
effect that there are frequent casein where bright intervals betn* 



I 



Dec. 190G. Spedroacopie Ohaervations of ike Sun. 165 

f&iut. Fraunhafer lines on nrcumjieiiumbral ragiona seem to be 
continued whhout diiuinution at bri^litnesA over thu umbra. The 
meaning r>f the ohFiervatiou is hy 110 meant^ clt-ar. 

In my incomplete knowledge of th« literature of the subject, I 
have not yet fuuntl w]ii>t)iPr it 18 already generally recoKnisud that 
maiiy liuee can W secu t« be darksuud over coasiderable rej^iuiia 
outside tbe penumbra. Kor iustancei, the linea attributed to iroo 
^L_wave-letigLh!i 

628083 

6298"oi 

630172 




ave on several occasioM been seen to be darkened over circnm- 
penumbral regions to distances amounting to two or three diametore 
of a large spot, i.e. to distances comparable with two or three 
minute* uf arc. 

The exteniiive floconli, which Hale bos disclosed witb his 
splendid riper. trobeli^graphic rernrdft, nhow that thn npot projwr in 
but a small part of the wholo area of disturliance. We may 
reasonably expect lines to be afiected over rdgioos cuinparaMo with 
tbe area of such tlocculi; and iu attemptln^toget spectroiielitigraiiliic 
records in the light of tJK! iron llneA, it would he well to 
distinguish between iron lines whicli show circtim pen um Ural 
darkcnin;; and thoHe which show no Much darkening. 

Of tbe reality of tbe phuuomonoii I have bevii able to assure 
wysftlf by observing the spectrum of tbe circumpenumbral regions 
without having the spot opon the slit. The darkening of the 
lines was detected, for instance, in the case of a spot having a 
penambtnl iliauictcr of 40*, and wur noted as being quite marked 
when the pt-numbra was still 4o"-5o' from the ulil. 

Mr Evershed, whose attention I called to tbe effect, told mo it 
vas one of those phenomena which he had recognised, but had 
felt unsuitable for systematic n^cording heoatUH the more one 
tried to hx it, the more it evaded one's power of recording. 

It is dilticu)t to knuw whether to interpret it as a true 
darkening of the lines, or rather as duo to tho brightening of the 
continuous spectrum. 

Il will be noticed that one of the lines 6301 '7 ioatanced above 
as exhibiting this circumpenumbral darkening is one of the 
linea used by iJan^r iu hiii spectroscopio determination of solar 
rotation. 

On several occasionii I have been able to aee 
of tbe outer and dark edge of the pcnui 
identical with those seen in the umhrn 
ou^t to be of importance as bearing 011 
form and level of suu-sitots. 

It does not seem oecewary at prew 
ware-lengths of lines ob<wrved as aff 
have been recorded by Fowler, Corti 
tions aupport tbeire iu a vaet uumb 



i66 



Mr H. F. Netcall, Notes on tome 



LXVII, 



:i 



to stutiag that, after a good deal of prelinunary study, I devoted 
tnyaelf to the careful recording of litiM aftected in the t*gioTi 
C-D, as soen un five good observing days, with the equatoiial 
equipment, I have compared theao records with the pbotograpliic 
rei^xtrds obtained with the horizontal dr|iii[)iiieiit, aitd have foond 
tlint the photoj^^aphs contain evidence of mo]« " affecteti " lines thAH 
were auen visually. They atau contain uvidence (which has not 
been yot systoinatttied or exhaiiitled) of the difference between thA 
ways ill which Hues are affected over the umbra, the penuinbra, 
and the circuiii[)etmtnhra] re^iuus. 

Out of I30 lines which In the visual observations with the 
eqaatorial equipment were recorded a« "afl'ected lines," 1 
that 

66 are entered as seen in the umbra only. 
20 are seen darkened in the nmbm and penumbra. 
5 are entered as darki-red over circuin}>enuin)iral regions^ 
7 are recorded as obhterated. 
3 are re>;ardeil lut exhibiting true widening. 
[9 appear to belong either to the urabrat or to the penumtnl 

group, but thi>' records are indecifiivp. 
10 are recorded as unidentiHed with Fraunhofer lines. 




tniifl 



Photographic records have been secured of the sun-spot spec 
from 5100 to 6700, thanhs to the excellent pinocyanol-liathed pUtae 
of Wratten and Wainwright. Plate 3 is a photogmphic reprodue* 
tiim (untouched I'y band) of part of one of the original negatives. 
It serves as a specimen i>f tlie kind of material obtained in the red 
re}{ion of tbe spectrum, where the selective absorption of vanadium 
is very marked; no le.ss thati 10 of tlie lines which are iuteniified 
over the umbra, are due to that element (Kowland's ideutifi cation). 



Remarkt tm. Widening and Darkening 0/ Affected Linme. 



J 

erfifl 

terafl 



Had the observations of sun-spot spectra been restricted 
those made with the horizontal equipmfint and the more ]iow 
spectroscope, I sbciuld have unhesitatingly said that the 
" widening " waa a miHUOtner. Most of the lines that attract 
attention as characteristic of the siinsput spectrum are lines that 
are faintly rcpreaentod iu the (Fniunhofer) spectrum of the 
neighbounng solar surface. The observations at Cambridge are 
ou this point in agreement with those of Professor Fowler and of 
Messrs Hale and Adums. But the " nfieijted " liues seem to 
to be darhmed rather than leUltmed ; so seldom do tliL'y appear 
be widened when seen through the powerful sjiectroscope, that 
have bM>n tempted to think that the few outKtandtng casee of 
apparent widening, would, with higher poM'er, be resolved. 

Both visual observations aud photographic records alford strong 
evideucc of this. IMnte 3 exhibits many instauces of linee that 
stand out as umbra lines and are qnite as sharp as any Fraunhofer 
lines. I would maintain, not that apparent widening docs not 



.1 




iMTMLV Notices of R.A.S. 




Vol. LXVII. Plate 3 



O 



m 




tec. 1906. Spectroscopic Observaiwns of the Sim, 167 

Eiat, bill that widening is not a ebaractemtic peculiar to bud- 
}t spectra. Tlie widening due to the i>\nuiietrical wings of 
tbe itiaf^niitiium lines at b is mure nmrktrd ^eueriLUy over circum- 
peiiiiiiibrHl regions thnii over ttii; umbra, acxnrding to my ol)serva- 
tioii» i\\\* sMmtcitiW whilst the revf^rfte is more generally true of the 
sodium lilies at I>. The three lines recorde<l in tli« la«l tiectioD a£ 
«xhitiitiiiK triii: widening are nil calinnni \\uf.». 

A gcMxl typical inaUnce of wliai I refer to is afTorded by the 
lineal 6306. This line has been de»cribed as "gcnvrally much 
widened." It i« often entered as due to terrestrial oxygen, 

tRoffland'a identiticatinn i>f tlie line 6306034 being accepteil. 
Professor Fowler has ascribed it lo scandium. My observations of 
the Hue with the equatorial uquipiuunt 6U|>])ortvd the idea of true 
n-ideiiing (in sjiite uf its unsy in metrical nature) to such an extent 
that I find in the diai-)' noteit the following entry : " 1906 Jnly 18. 
Umbra line at 6306 studied carefully. This ia a strong liae and 
aometinies looks like a iiuich u'Ld*:ned linu, ttouietiiues looks more 
A8 if it [Rciwland'.s \{0) lino] had a dtirk line near it. To-day 
it ceruinly VuiVk like true widening, thu only caso of widening' that 

I I am quite sure of yet." 

It hardly needed mo^re than a K^axce with the more powerfd 
spectro»cope of the horizontal equipment to decide the case 
•Kaintt widening. The fact is, a new line Qp[)aiini in the .speclrum 

[ of the umbra on the violet side of the oxygen line. Even the 
photographic records show the line as double. Measurements 
give the wave-len^'th of the umbra line as 630586, whilHt the 
A{0) line has wave-leiiHth 63o6'02. Itowtaitd givcj* a Fraunhofcr 
line of intensity 0000 at wave-length 6305-^78. It would be 
intereHting if this turns out to be lh(> scandium line which 
Professor Fuwiec finds iu Thalen's tables. 

These details have been ^ven becuu^c they bear on the 
general quentioti of "darkening" verstu "widening" of Bun-spot 
line.s; they bear alsfi nn the rimon.i coincidence of telluric lines 
with atlected lines in the sun-spot spectrum, to which Father Cortie 
and other observers have referred. 



Band* in Vu Spectra 0/ Sun-tpott. 

Swtpected Fluting in the Green Reffifm, 5000-5168. — Ther« 
are many iitolated lines conhned to the umbra {e.g. vanadium UneB] 
which cannot be yet put into the category of elements of a band 
or fluting ; for criterion as to whetht-r a given ]in« is isolated or an 
element of a band, we require analyai* such as Alexander Herschel 
was the first to suggest and to apply, and such an l>eislaadre» has 
applied with such success to the band*.)d spectrum of nitrogen, etc. 
Still, as a first attempt, the observer n led by a aort of instinct to 
pick out lines as belonging to a band ; and in my earlier observa- 
tiooR in 1905 December and 1906 January, I devoted M>me time 
to the study of umbra lines in the region 5100 to 5 168, estimating 



168 



Mr H. F. NevftUl, Notee on $ome 



LXVILl, 



Wdve-IcD^ths witb a view to att«mpUDg to determiiMj the pnbabb 

cbemicat ctri^ia of the Suting. 

It wfts Bt once evideiiit that my oWervatJons confirmed Fowlef^ 
Tiev that the Hntwi which seemeii to be speci&Uy cbaracteriiitic (rf 
the suu-spot apoctruu were in reality alaa feebly represent«d iu Qtt 
solar specirnm. 

The lines do not agree in position with Rowland's carbon Vrntt. 
nor cau thej be made to agree either by t]i8 assumptiou of same 
displacement common to all, or by the aitsnmptiou that the 
observed dai-k lines arc intervals between bright lineA. 

I expected, by plotting the estimated positions of the liaea 
carefully on an enlarged reproduction of Rowland's map, drawn 
(on a scale of i cm. to i tenth metre) on a papier millimetro scale, 
to i^t values of wave-length truBtwortby to the t«ntli of a tenrh 
metre — awuracy sufficient for iduntilication of the fluting. The 
reconled ponitions were read off with eare to the hundredth of a 
tenth metre, and I int«nde«l to discard the KKcond decimal. But a 
comparisuii of uiy reaulta with the mean Taluea which vnett 
published shortly afterwards by Hale and Adams, as determined 
from their betiuttful photographs of sun-spot spectra,* showed tai 
unexpected precision that it seems well to record the expcriet 
for the benefit of observers who might use the method in 
absence of refined micrometcn. 



PboloETaphic Mt«iiirca, VUiul K«Un»t«f 



5*3583 

38-58 
38-96 
40'44 
41*40 

43 Sj 
44 'a I 

45 "93 

45 "93 
49-67 

49*99 
50-36 



It. 



3650 

36-65 
38-59 
38-97 



Ji*it 



41 -48 

43*°! 



47 ■9* 
4889 



Pill 



otomiihti! H«kiur«t. ^In&l Eatlaul 
tlM* and AdaSDi. N. 



5030' 

50-55 



5'S'37 
5163 

S3 -8a 
56-53 

S7«> 
5779 
58-81 

59*96 
60-39 

63*10 
6379 



52-28 



5653 
56 74 



6o-li / ' 

63-11 I * 
6359 



pair 



My attempt* to find a known llnting that will correspt 
the Unas recorded in the table have been hitherto udbuo< 

' Ailnphi/9. Jour, zxiii. it-44) 1906. 






Spedrosec^ie Ohservations of the Sun. 



My utimaUs of the wave-lengths agree more closely with Hate 
and Adams' niQa)«uro8 thaa with Mitchell's obeervatioua. 

SutpteUd Fluiings in the It&i Region, 6370-6390. — The 

groups of Hnes rerordod by Young, Mitchell, Cortie, and Fowler, 
as ttL-«ii in the red region of the dpectnitn about wave-length 6381 
and 63S3, huvt' bucn tiLudied carefully ou several uccafljoua ; uiid the 
set of obaervatiom made with the equatohal equtpmenc on July 30, 
1906, have ^ircu the fulluwiitg data for 21 tiues between wave- 
lengths 6377-6393. The meaanrea given in the last column were 
le on a photograph (H.S., 208} taken 1906 A.ugQst 31. 

6377*81 Dark line 3 

7S15 Narrow hriglil 
■treok 

78-48 Dark line 3 

7894 M 4 

79-64 

80-31 

82-65 

83 i^ 



170 



Mr H. F. iVctca//, Noiti on some 



LXTa2, 



towardtf llm violet, aoiJ with its li«ad not far from wave-length 
5210. Attempts to determine tLc posiliou uf llio head od two 
different AayR led to the following results : — 



1906, Aug. 1 1 

..31 



5210*2 

5211-0 



This dark hypothetical Hutitij; i» recorded **as quite marked at ttaa 
and not an illusion due to tbc proximity of Frauuliofer liuee, (or 
ttie K f!roup is not so atferted. The part of thu Npecbnim between 
5310 and 5300 ia the darkest part of spot spectrum in the re^oo 
between 5100 Hiui 5300." 'I'liis fluting is at 11 region where there 
are many umbni lin&i, nnd had the appcRrnnce of u d&rkening of 
the unresulved background of the spot specLriim. 



Laboratory Experiments on Resolution of the Baek'jrouml qf 
Are Spectra. 

Probably all ftpertroBcopinta have n^alised that, in studying the 

arc spectrum of, let us say, iron, they concentrate attention upwo 
the bright lines of iruu atid couuotit to dii^regard the "continuooti 
background'' on which the lines are generally seen. When, how- 
ever, powerful spectroscnpcB are used and attention is paid to the 
baekgronnd, it is ^eon to be resotved into tine lines under conditions 
which are generally not (iuit« under the control of the observer. 
In many cases the lines show signs of arraugumeut in bands and 
llutings ; in other coses the signs of Htrocture of that kind are nt't 
detectable. 

The resemblance of this varLeil structure in the background <rf 
bright arc r^pectra to the structure that ia visible under what wt 
are tempted to call the Eineat conditions of seeing in tbe spot 
Bpectmni, must Lave struck many oheervL-rs. At any rate it 
caused lue no surprise when, in the spring of ihifi year, I gathered 
from Mr Fowler that he bad been looking for detail in arc spectra 
similar to that which bad led him to identify some llutinga in star 
epecttu with the reversal of the Hulings discovered by him in tbn 
titanium spectrum and attributed by him to oxide of titanium. 

I have, both before and after my conversatioii with Mr Fowler, 
secured a few photographs of the background of some arc spectra 
with B vi'ry powerful grating spectroacope, and have compared some 
of the details exhibited on the photographs with the fine structure 
of the sun-spot sjiectruin. Ho far 1 have not had miich KUcoess is 
finding similarity. Rut in one case I find resemblances which call 
for further investigation of the sii'rt ; for bright flutings degraded 
towards the red have been found in the spectrum of the arc 
between iron terminals, which had been tippeii with lime, — 'fluLingi 
which coincide in position and direction of degntiiation wil ' 
uneyiu metrically winged lines dnrkvued in the suu-Hpot specti 
close to the wave-lengths (a) 5504 and (b) 552S. 




Dec. 1906. Speclrosa}ine ObaervatioHS ofUht Sun. 



171 



I should add, however, tbut T have found no Gutings recorded 
by other o1)5erv6r8 of sun-sput spectra at these wave-lengths. 

MitchttU's obaervation^ agre« with titose of HiiU and Adams 
with respect to darkened liaea near one position (a), bat not in the 
aecood case (b). 



Mitchrll. 



fSS^M'ls Ti Djirk«ned 



ofia 



._• I 06*10 Ilia (it-nnrallr mnch o6'io 
'"^ .iarkeued 



07-00 Fc WiagKl 



07*00 Wingad 



m 



S 523 -66 

3577 



a»ry 



Dtrlcatied 



»73 

37-80 
99-38 



Search /or Etridmee 0/ Local Convection Ourrenis on the 
iSim'n Sur/aee. 

Oq many oocaaions when we were uaing the equatorial eqtiip- 
inent, special attention was given to a search for violent motions 
in the line of sight in the neighbourhood of sun-spots. In 1895 I 
spent five wrcIch at the KifTclberg, niakiti;^ flpeetroecopic obaprv.ati<ms 
of the Sun's surface with a gi-atin<; spectroscope. Sevend times I 
fottnd evirlences of violeitt local downrii?ih(>H of byilrogen, which 
were detected by what one may call isolated islands of the C liiie, 
showing large displacemont towards the ultra-red. These down- 
rushes of hydrogen wore indicated by a dot in the spectrum, and 
the absence of other general darkening of the spectrum proved 
that thoy were not connected with any formed sun-spot. They 
persisted on two or throe occasions for many hours, and could 
easily be picked up by allowing the solar image to trail across the 
slit uf the spectroscope ; the small black islniid uf C line would 
middenly ttush out nnU in an^'tbor moiucnt be gone^ unless the 
tintliuRof the image wwre stnpppLl. Some cnrreapondence that I 
had with Dr Vogel and l-'athwr Sidgreaves at the time, k'd me to 
the vit-'w that the phenumenoti was unusual. I had, withor^*' -**^<4t 
success, tried to connect the positions of the down' 
hydrogen witli pnjiitioiis iti which spots api>enred later. 

I made fiirthar attempts during the (last sum 
similar phenomenn, but though I regularly exao 
surfo^ in this way with the equatorial equipu 
operation of trailing the whole surface of the 81111 
30 minutes to complete on each day that it wu 
could detect a single instance of the occiimi 
dowurush. It njay be pointed out that It ta j 



1 72 Sjieflmscopk Olaerwdions of the Sun. LXVn. 2. 

the period of the eun-spot cyclt — since the previouw ohscrvatjomi at 
the Riffelberg diacloAcd the apparent frequency of the iihentmicnon. 
Tbc ubsurvations, however, serred to sbusv also how scldoui it 
occurs that largu iliHturbancas t>f the kind tliat would bo detect^ 
hy distortion of the liiiea in the specliiuu are to be wen on the 
Sun's surface. BelopoUky has catlt'd atte'iition to this point in 
hiH note published in vol i. of the Tmnsadionti of IJie Union for 
Solar Ueiwarch, If thla observntion is further corroborated, it 
would tend to show that the violent convection currcnta, which 
we believe are needed to keep up the supply uf radiation from the 
Sun's surfacp, and which are so well brought to mind by Professor 
Schuster in bis Oliwgow lecture on aolnr evolution {A^raphyg. Jour., 
*vii. 173), must be confined to Btmtii l«!ow the revendng layer. 
Tliis is a result which it seems difHcult to reconcile 'wilU Other 
considerations. 

I have great pleasure in acknonledgin;; my obligations to 
Mr W. H. Manning for his efficient help in these observations 
uuder c ire musts nces that called for much patience. 

To Mr J. B. HubrccUt alao, whom we ore glad to have at the 
Observatory, working as a research student in astrophyaics, 
I would here rondf^r thanks for hia help on many ocuuions when 
be bas been at hand making preliminary' observations for a 
determination of the rotution of the Sun, to be derived from 
photographic records taken in the spectruacopic method. 



MONTHLY NOTICES 



OF TUR 



ROYAL ASTRONOMICAL SOCIETY. 



Vol. LXVII. 



January ii, 1907. 



No. 3 



I 



W. H. Mav, BBq., PRraiDKsrr, in the Chair. 

Rodney Bojee. Soadan Surrey Deportment, c/o Royal Colonial 
InBtitute, Korthumberland Arenue, London, S.\V. ; 

Arthur CUmiusou, I}ei>uty Cou)BiiBsioa«r of Landv, Lagos, 
West Africa; 

Oeoi^u Innes, M.P.K., Olive Bank, Liberton Brae, Edinburgh; 

Arthur Kfut Lucke, Suez Canal Com[)any'i Serrice, Tniuit 
iJepartment, Ismailla, K^'Vpt ; and 

GeorKu -Street, M.A., Merton House, Southwick, Suatiex, 

were balloto'l for and duly elected Fellows of the Soeiety. 

The following candidatoe were propoaed for election at Fellowa 
of the Society, the names of the proposen from pereooal knowledge 
being appenrled : — 

EtlwarJ George Btor<mfiHld Barlow, Dittun Lo^l^e, Stourwood 
Avenue, Boomemmith (propootMJ by Col. K. E. Markwtck) ; 

Lieot. F. G. CoopL-r, B.N.R., H.M.S. Otxan, 131 Suttoa Court, 
ChiBwick, W. (propoMd by E. W. Owens) ; and 

Edward Powtr, F.8.A^ F.G.S., 16 Sovtfawvll 0«rdenj., S.W., 
and Watcnhip^ ^'evbtuy, Berka(pnqM||^by "W. S. Franks). 



Fifty-ooa pnwnte wm sni 
■ince tha laift BMtisg, incloding. 

W. H. Pickcridg, Luiar « ' " 
paied, praaaatcd by Ihn lU'. 
Chart (^ the bcanna, prsaot' 
wich ; Knfranng fnxa poftr 
for the Rc^al Sockty, prtamt^- 
Portrait Pofkd. 




<74 



Ferturhations of ffallej/s Comd. 



LXVILJ. 



The Pfirturhationji of Hallet/e Comet. By P. H. Oowoll and 
A. C. D. Cruiumeliu. 

Shortly after tlie December meeting we decided to nndettake* 
jointly the computation of the perturbationB of Halley'a Comet, 
Wishing to ascortain as rapidly aa possible wbetber PontikouUat'a 
date of tbe next puriholion ptiaaage (1910 Afay aj) w&s approxi' 
luately corracL, we made a prelimiuar}' cumputatiun of the Jupiter 
perlurbatiuas, dividiiij^ the comet's orbit into eighty portions, and 
cloaelj follovring Pontikoalant's method. We introduced, hoireTe^^| 
two moditicfttionK, which we think ore improTementa : — ^| 

(i) Pontdcoulant has made hia computation needlosaly long ^ 
the retention of a ouoibcr of ineanin.Lilesa and piiperSuoiis figurea; 
thus he doterminoe the perturbing forces X, Y parallel to ^e 
principal axes of tbe elUpne to two places of deamals, implying as 
a rule, three si^^inificant figures ; but the product of these, by the 
factor reduciDg the perturbatiun to aocouda of arc, is given to six 
signihcaat figures, of which only three can bo trusted. We have 
reetrictBd ourselves to tbe reliable figures, wliicb involves no low 
of accuracy. 

(3) Pont^ootiUnt performs the multiplication by these factors 
separately far each element of the oibit. We have first taken ths 
sum of the components and multiplied by the reducing factor ouc« 
for alt lit the end, tfiUH saving much labour. 

Wo are uow undertaking a more accurate investigation of ths 
perturbations, ttiviiling thn orbit intn iSo pnrtions, and inciading 
the perturbing eflect of Venus, the Earth, and Neptune, whidi 
PoDtiicoulaut did itut consider. We Ibtirefore deem it unnecessary 
to do more at present than give the two main results of our pre- 
Umiuary wurk, ^rhicb are as followti : — 

(t) 1910 May is the correct date within a month for the next 
perihelion passage. Oiir actual result is a fortnight earlier than 
Poot^coulant'*, but we lay no stress on the difference. 

(3) Our computations confirm the suspicion ezpraMed in 
December, that Pont^icoulaut's value of the eccentricity in 1910 
is notably in error. In fact, we make tbe perihelion distance 
appreciably th<^ same as at the lest return (0*59}, whereas he 
increased it to o'6S. This change is of some Jm[iortanoe^ as it 
would cucisiderably atfect the geocentric path of the comet at tbe 
next reiurn, and would also considerably nio<iify the point at 
which tbe meteors atcumpanying the comet would interact th( 
Elarth's orbit. 

Hesult (i) indicates that Angstrom's curve fails utterly for 
next return, and throws much doubt on the n-ality of liis 
inequnlitius. Possibly many of (lie enrlier return? of the c( 
have beeii wrongly identified by Hind and Angstrom, aacL 
lalter'a curves may thus be erroneous. 



I 



I 



I 



Jan. 1907. On the Errors of a Photographed JUscau. 175 



On tlis Krron of a Photographed Rhean. B7 W. H. M. 
Christie, A. S. Eddingtoii, and C. DftVidson. 

The iavestigation which in here described was undertaktm in 
eoctnectioii wilL iha disciissiuu uf thu rusulu of the Grceufricb 
photographs of Eros 1900-1901. The determiaaCioa of Ibe 
diviuoii ern>n4 of the reneavi as iuipriDted on tho photographic 
pUtea to the very hi^^h ilegreu of accuracy roquireil, is iu some 
reapactA a iieiv problem, m that flome of the methcMttt ami roonlts 
may be of interest. 

An account of the preliminary detorrai nation of the errors of the 
r^eeau (Nf>, 90), which was used for all tlie Kroe photoj^raphs, 
is printed in the Introduction to the Astrographic Catalogue, 
Greenwich Section, vul. t. p. xxxvii. These provisional division 
ernirs wure applied in t-bv rudiictioii of the tikvasiireK of photographS) 
but a timch more oxteiisive investigation wiu* felt to be neoeasary 
in onler to deduce a trustvrorihy value of the solar parallax from 
the reitults. 

A preliminary mmparixon mado in 1903 between the nJseau 
itself nud photograph:* uf it on seven plates had sbowu that there 
were sensibUt differencns, which called for further dlAcnsftion after 
the heavy work of measurement of the Eros plates bad been 
completed. It may here be explained that tlm ri'raeau \a imprinted 
on the photographic platu by parallel rays from an electric lamp in 
the focus of the 13-inch object^gUss of the Astrogiaphio telescope, 
the n^fleau and the plate being mounted face to face, as nearly aa 
possible in contact just outside the object-gluss. It is to be noted 
that the parallel rayti ooceiisarily pass tbnjugh the gltiss of the 
r^ouu from the back hefon.- falling on the silver film. 

Under the ordinary conditions tliu reseuu ia rovorsod with the 
tolescope in passing from east to west of the pier, the same edge 
of the plat« being in cuniitct with the hearing studH, on buth mdeti 
of the pier. In coUB^quence of this reversal the division errors of 
the central lino 14 and the mljucont lino 13 or 15, hctwoen which 
Eros is usually placed, affeot the II.A. of Ems with opposite signs 
on photugnphs taken with the telescope east and west of the pier 
respectively, and thu? directly enter into the value of the parallax 
deduced from inomiog and evening photographs, with telescope 
east and we-st respectiTely. 

It was therefore necoiwaiy to determine the division errors of 
linos 13, 14, 15 with a degree of accuracy for beyond thr "t 

lor the other lint--8. 

What was require<l in this new investigation w 
that part of the roseau where Eros falls, ref> 
that part of the rr-caa on which thost! it 
co-ordintilva of the plate centr; were (led 
results thiw*i series of placM of Eros liat 
AstTographic photographs using nr/r' 
of the centre ; (j) Astrographic pbc 




I 

» for 



176 Sir W. Chri^U, Masi-8 Eddington arid Davidson, ucvn. 

selected within 25* of the centre : (3) Thompson photographs 
comparison »tare. In serieH (2) tbu coiupariiioQ slarei may l>e 
coutiidered to be, iu tlic lueaii, fairly uoiforaily diatnbuted over lb« 
square between the lines 9 and it) in eao.h co-onlinate ; while in tbe 
other twn nories the fttars were di^tribnteil orer the squere between 
lines 4 and 24. DlU'ereiit con'tictiuiiii inuHt be applied to Kroe in 
tbv Iwu L'a^ba. 

Thcrti were three steps in the determiotttion :— 

(1) A tnoT*! jiccurate lueasureEiient uf the errora of linea 

14, 15 on the silver rt-sL-au. 
(3) Meneurement of the systematic differences betveen prints 

iif thii rL^seau and th« rcseau itae]f. 
(3) Kxatuiuatiun of the stmighlness of the ruseau lines. 

As the declinutions of Erne are not very important for parol 
only the ernirs in x have so far been investigate!. 

1'he numerical values of the errors given in this paper are for 
the Bcak' of the Astrographic telescope {i*"'"= 1'). They must 
halved befure being applied to the Thoin])&oii phoUigraplia 
n^seau was printed ou ^joth sets of ^hoto;>raphs at the same time' 
and in pnici»ie)y the ^ame manner, the object-glass of the ^Vstro- 
graphic telescope beinc; used to give a beam of parallel raya. 

The microuieter uncil throuyhout was described in i/.A^, »oJ. 
liii. p. 326, but hus been somewhat modified since then. Two 
microscopes, whose di»tAnof apart can be adjusted, are connected 
by a bar which can move longitudinally in a nlide. The r^seaa 
and scale {or photu^nphic plate) to be compareil ore carried in a 
large frufuc, so as tti be viewed one by esch microscope. The frame 
can move in a slide perpendicularly To the line joining the 
niicroscopea. A flxed wire in the right-band microscope is set on 
the required scale division (or other mark) by moving the bar 
whirh carries the two micrfiscojtes, by means of a slow-motion 
screw. A movable wire in the left-hand microscope is then sa^^H 
oa the required n^sonu-linc by turning a micrometer-head. Io^| 
order that the same reading of the micrometer may always corre- 
spond L() thu same dixtauce between the two points viewed, how- 
ever the slides are moved, it is necesHiry that either the axes of 
the microscopes should he immllel, ur that each slide should move 
accurately in its plan*'. Pmhably an appreciable enor arises from 
the Qon-fulfiLmeut of these conditions vlien the outer parts of thi 
r^eau are viewed; the error cun be detected and eliminated 
turning the riiseau through iSo" and ns measuring. It seems 
be inappreciable within the area between lines 9 aud 19. 



(i) Corrections to the mlopted division errors of tinea 
I3> I4> 15 on tlie silver reseau. 

In the original determination the division errors of Hues S, t^ 
and 20. referred to 7 and 26, were (irst determined (along y=t4 
by comparing the intenrals, a-8, 8-14, 14-ao, 20-16, with 




I 



I 



Jan. 1907. On the Errors of a Photographed Heseau. \yy 

SMiie interval oq a glass scale. Tho erron of tbu iuteniioJiate 
lines were then deter mi nf^<i hy the .symmetrical method explained 
ia the Introduction lo the Astrographif! Catalogue, vol. i. p. xxx\ii. 
Ill the re-detemiinatioii, the object aimed at was to refer, with 
tho sreatfiiit accuracy attaitiahlc, the central tines on which the 
place o( Eros de[»end» to the nieaos of the hues used for reference 
or coinparisoa etare, 4 to 24 or 9 to 19 respectively. Witb ihia 
object tho interval between line 14 and each pair of lines from 
4 to 2 4 wn.t compared by means of the glass scale at ^ » 13'$ and y » 
14*5, 00 that line 14 was referred in succession to the pairs of lines 
4, Z4 ; 5, 23 ; 6, Z2 . . . . 13, 15, giving, after application uf the 
pniviiiioiial divisional errors, ten independent determi nations of 
the division error of line 14 referred to a pair of lines. Similarly, 
line 13 was referred to each pair of lines 3, 33 ; 4, 24 .... 12, 
14 and line 15 to each \mx 5, 25 ; 6, 24 ... . 14, 16. Since, 
in tliip method, each line is neot-ssarily referred to pairs of lines 
sjinmi^triciliy sitiiati^d ahoitt iti^eU, lines 13 and 15 conJd not be 
referred exactly to the same lincii (4 to 24) as line 14, huL it Is 
clear that the acddentul residtiat division error arising from the 
aubstitution of line 5 for line 24, and lino 25 for line 4^ in the two 
cases respectively, is nef^ligible in the means of 20 lines. 
M The investigation was carried out at //=13'5 and i/ = i4-5 
independently. Ttie accompanying table gives the result. 



TaUI^ I. — CoKREOTtONS To pROVISIOKAL DiTlSIOK RaR0lta> 



kL 


1=13. 






i:-i4. 






*=ts. 




^(errml 

la 

IJne*. 


CorTftcUiHi. 


lUrerred 

to 

Ltoei. 


CorrMUou. 


to 
Line*. 


OorrocUoe. 

(, = 13-5. IfaliJ. 


3.33 


* xx)3 


■04a 


4.24 


foS; 


+ ■02^ 


S. 25 




+ ^33* 


4,32 


■t- -026 


■000 


5. 23 


+ ■063 


+ \304 


6, 24 


f '016 


+ ■031 


S. 21 


-■CXH 


+ X>18 


6, 22 


+ XB5 


+ -046 


7,23 


- -008 


+ "ooa 


6. 30 


-■OIS 


-•014 


7,21 


+ •004 


+ -ooi 


8.22 


■031 


+ •015 


7. '9 


+ •021 


+ ■028 


S, M 


- 'Oil 


-•034 


9.21 


- -048 


+ •008 


8, 18 


- -027 


- IMS 


9. 19 


+ •004 


- •001 


10, 20 


■047 


4- -014 


9. »7 


-009 


-•035 


10. 18 


+ -006 


4X}|6 


iUL 


.^n 


+ ■005 


10, 16 


- -020 


+ •010 


11,17 


- -046 


-VWf 


'^^PV 


41 


^^ 


11. IS 


- "024 


- -018 


13, 16 


- -oil 


^•(^:: 






^W 


13. 14 


-033 


-M27 


13. >5 


+ ■Dt6 


- 'pi . I 








leans 3 to 33 


-008 


- -013 


[ 4 to"4 


^■014 


i 'u, 








(UQS 8 to 18 


-•023 


-023 


1 9 to 19 


-006 











The two seta of niean^ given arc th< 
applicfible to Kitw when referred to rff^ ■ 
respectively on Astrographic phot^L' 



178 Sir W. Chrittie, Messrs Eddington and Damdatm, ucvxL 

It will be uotioed that luie 13 lias a consideMhle bend ("'04) 
in p&6«ini; fr<)ni y'=t$^ to 14^, whereas lines 13 and 14 an 
aenstbly straight. 1 




(a) Systematic differenetx bttwsen the r/'tieau and photo<pxtjjlu. 

Fifteen platen were selected so &i tu be well representative of tfa9 
different batches of Eros platefi. These were one by one compared 
with the nilver n'spau ; ti>f< corresponding liiiefl rni plnte and rMeao^^ 
being compared at i/=- ly^ and at y= 14'$. All the x liooe fpHi^^l 
3 to 25 were meaaured on each plate ; u selection from tlie retiulta U^l 
given in Tubles 11. and III. Tlie frrors tabulated are referred to 
the means of lines 9 to 19 as zero. They are differences between 
the prints arid tlie silver nsttean, and consequently are ad>iitioiHl 
to tlr' eiToi-s of tba ri!'seiin itself. A linear term (corrviipn tiding to 
an apparent diffen-ncn in trciilu between the plalo snd reseau) has 
been removed from the resiilt" for fach jilate. Thin is neceMary if 
the plate eonntHhtA a and e, found with the originally adoptsd 
errors', are not to be modified. This correction for scale is given 
the lust column of the liiblea fur ten ruseau intervalit as applied tffi 
line 4. and with reven^cil sign tu line 24, and proportionately to thtti 
other lines, and has been applied in forming the resulta given. It 
was determined by comparing the mean of lines 3 to 13 with thf 
mean of lines 15 to 35, giving equal weight to each line, tl 
cxirroxpond with tlie ^lyslutu mJopCcd in forming the plate coastanta.,! 





Tablk 


li.— CyMi'-VKiBox or 


pHDTOOaAfUlC 


PatKTH WITU 


Ktou 


"^ 1 










*r 1^=13 5 








1 


PIsU 
So. 


3 


4 


I* 


"3 


M 


«5 


tft 


■4 


•s 


Corr.0 

Sod*. 


5t6o 


-13 


-'-OS 


• 


- 'OI 


- -oa 


- •oa 


■ 
-■03 


■ 


-"■21 


+*^ 


S172 


- '11 


-06 


-•05 


'00 


- -02 


-■03 


- X>I 


+ ■01 


- 'WJ 


+ -j| 


5183 


+ •14 


+ T4 


-•06 


- 'lo 


-06 


•04 


■oo 


+ •26 


+ •04 


^i 


5190 


•OQ 


•00 


-■05 


■04 


-•04 


•00 


-■03 


-*i 


- 27 


+ 132 


SM4 


- -10 


- V2 


+ *03 


•00 


- "01 


-•08 


-•06 


+ •21 


-05 


'*''ik 


5218 


-19 


' 09 


+ •02 


-07 


-OS 


-05 


■00 


-•07 


-■ao 


+4 


5230 


-109 


-05 


+ ■02 


-03 


-•05 


-•07 


+ XM 


+ •02 


- -11 


-t-9 


5*39 


•09 


- '01 


- 'Ol 


- -02 


- "02 


-■07 


+ •03 


+ •09 


-•»5 


+» 


5260 


■03 


^•01 


+ "Oi 


-•05 


- ^ 


+ 04 


+ ■03 


+ 03 


-*s 


-1-9 


5*83 


-■|l 


+ ■12 


-•05 


-•05 


-VX4 


-■07 


- "01 


+ •13 


- MI 


-tj 


5307 


-•39 


-•08 


-03 


-■04 


•06 


- '02 


-x>s 


+ tti 


- -IQ 


+«| 


53*4 


-73 


-•39 


+ "03 


- "02 


-•07 


■06 


■'i 


•08 


-•3fi 


♦ ••7 



5336 - 108 - 06 



535* 



•33 



"06 



■18 + 03 



J368 + -42 + -36 - -03 



OS 
•06 



•08 

■04 



■05 



■00 



'oj +*o8 
•06 - "Ol 

"07 +-27 



-08 

'23 



m 


r 










•^ 


H Jan 


1907. On the 3rron of a Photographed 


BiMaiL 


379 1 


^ft Table IIL— Coiu-ijutint or PBotf»hAT«tc Paxtm win IUbuv ^^^M 


w 






" r=M'5- 






^^H 


TMa 


] 4 


t* 


■J M tS 


i4 


•< "S 


Omt. fep ^H 


5160 


- "ij - "04 


+"■09 


-■05 - "06 'Xa 


I-'tOI - 


"•05 -^i 


^1 


5'7» 


- 13 - X19 


+ x>5 


-•10 - •07 - 07 


■M05 - 


•07 -23 


H 


5183 


+ ^08 +T16 


-■08 


- -06 - -06 - '04 


•oo +raD 4-104 


H 


5190 


- xa +104 


4-V2 


- T)9 - TJ4 + "OI 


*-03 - 


- 07 - "33 


+ xA ■ 


5304 


-17 --07 


+ •10 


'•06 - "03 - -04 


-■03 +'13 - -06 


^1 


1 5a»8 


- 'la - -la 


+ ■01 


-•03 - x>8 - *oi 


- T03 + •04 - •08 


^1 


B5330 


-■12 -'II 


+ 08 


-•II --02 --OI 


+■06 


•00 - •32 


+•07 H 


P^pJO 


-107 -07 


- •oi 


- -06 - -05 - -03 


- -04 + -03 - -11 


4-Xl( ^1 


5260 


.105 +-05 


+ ■03 


+ ■01 - -06 W) 


•00 - 


•04 -T)9 


4-*OI ^1 


A 5383 


+ 1* + -13 


+ •01 


- '12 - -04 - -05 


+ ^02 + '09 + -OI 


H 


■ 5307 


- '39 - 15 


+ TD3 


-'13 -'O9 -"04 


+ •03 - 


■08 - -25 


+107 H 


B53Z4 


■64 - 43 


+ 04 


- -07 - ^ - -03 


- "oa 


•07 --39 


+■38 ■ 


■5336 


-17 -'II 


+ 105 


- "04 - 103 - '04 


- "OI + -oa - •©$ 


+ yA ■ 


"^535* 


- -31 - ^9 


+ *Da 


--07 -T»9 -T)7 


+ -D3 - 


03 - -30 


H 


53« 


+ •39 +38 


- tn 


- MJ - "06 - fli 


+ -06 + -33 + 1((3 


-i^^^H 




Table IV, — CoxpAXiiwti or Fuotoorapub 


WITH IUmBAO. 


^1 


• 


IT. U'» 


UMAK KBSOIUS <V 15 PU(>T0OBl.riU. 
It, »4"5 « ». i3S ». MS 


Frobaltle 
Inw. 


H 






-''119 


35 -"13s 


-136 


±'■038 


^^1 




-'036 


-•047 


24 +-063 


4- -031 


±•032 


^^^1 




+ ■017 


-1004 


33 +'043 


+ 1017 


^•016 


^^^1 




- "026 


4*039 


33 +-007 


+ ■003 


±■013 


^^H 




-^3 


+ ^011 


31 - xttg 


+ •030 


±*OII 


^^^1 


8 


+ •056 


■f -040 


30 - vol 


+ •007 


±•011 


^^H 


9 


+ 1>29 


+ ■027 


19 +MIS 


+-•016 


±•009 


^^H 


so 


+ Xtt3 


+ ■030 


18 +'035 


+ ■008 


±•007 


^^H 


If 


+ ■011 


+ 1038 


17 +'o?o 


+ ■011 


±006 


^^^1 


la 


-•noft 


+ 027 


t6 - XH7 


+ •010 


±■007 


^^H 


■S 


-«40 


-■075 


15 --043 


-■030 


±•005 


^^B 


■4 


-■«M3 


-^s 


14 - *043 


-t>55 




* ^^1 


The lucau dilTureiiceii lietween the F^seau and ^ 
troni till! Gfteeu piiots examiucd, art; givuu in ' 
with the probtiltlt* i-rront of ihe valnea foaS' 
mean diiiconiance» of the fifteen printtt fur t 
will be seen that, far from beiog arrora 
H T^seao, the printa differ frDiu it verjr 




1 ^^1 



l8o Sir W. Christie, AfeJixrs Kddingion and Davidson, I.XTU. 3, 



i 



centre the printA ngroe very clnaely among themselvw. The meu. 
diaconlance of the measured position of a line on a njv/te pri\ 
from the m«an jiriut ranges from ±""oi6 for line 14 to ±''04 fi 
lineij 9 and 19, udcI to ±'13 for the extreme lines 3 and 25 
increasing regularly with the distance fritni the centre. The y»at 
variability of the outside lines is mainly due to the method hy 
which the scale correction whs found. That lliw irn-giilariiy is not 
entirely arbitrary can he very well seen by examiniug the 
differences between tlie errm-s of lines 24 and 25 in Tables 11. 
and III. Whereaa the nbsoluti* errors vary greatly from print to 
print, the diflTerences are very accordant. 

The correction to iJie place uf Kros derived from Table TV. is 
very considerable. If tt is nob applied tliere will be un npparent 
spurioufi parallactic displace meat of Kros amounting to about o''i 
lietween east and west positiotts, and itn error of at least "'025 in 
the final value of the solar parallax, deduced from the A&tro- 
gnphic photographs. 



MtH 



(3) Er'imitudimt 0/ the Straiffhtnet* of the Lines. 



I 



So far, all maasuremonta deAcribed have been confined to tbe 
strip of the r^seau near jj— 14. and the result enables Kros to be 
accurately refeired 10 HlarH distributed over this strip. But this 
atrip umy an tin* mean liave an error relative lo the area covered 
by the refertmce and comparison stars. If the ruling maclilue 
is not absolut«1y accurate, a curvature of all the r^eaii lines maj 
exist. Previous investigation had shown that if such a curvAtnn 
exists at all it must he very small, but it might nut be negligible 
in the present problem. 

The straightnesa was tested by comparing the lines directly 
with a spider web mnimted panillol Ut tiiem in the double fram« 
of the micrometer as fnr the rompariRonn of the r^aeau and photo- 
graphic plat^. Sir Liavid Gill bus described a somewhat similar 
comparison with a spider Line (Memoini S.A.S., voL 51), though in 
that case the n'seau line could not be compared directly with the 
spider-line, as woja practicable with the Greenwich measuring 
apparatus. 

In order to eliminate irregularities due to " knota " in tfas 
spider line, measures wt-re rejieatod with the spider lino turucd 
over front to hack. A more derious error (which was attribuUd 
to the slide which carries the spiderdine and r^seau not moving 
perfectly in its own plane) cuuld only be eliminated by tumtsg 
the r^cau through iSo' and moaxuriug again.* 

I'jcperinients were made both un the prints and the r^sean 

* Wbon thu r^d<.-su n turned throush iSo" the curvatsre or other 
irrcKuliritii* moMun-ii K^aiDBt tba apider-lino will W reversed in direrlion ; 
inBtrumciital rmr% wilE bo un&llorcd. The instninimita] «rrar soioctated 
with, asy, y-g r^MU direct will bs kuocUted with y~i9 r^Maa rev«r*e<|, 
»o that tint iiistnitiiKatAl error will not he t)imiui>li.-J Irviu Uic mdiridoal 
points, bat frum the means of pain of poinu such m y = 9 sad 19, and from 
the meao ctirrature. 



fao. 1907. On the Errors of a Photo^aphtd Bdseau. 181 

[itself. For the rdiieau the tovestig&tion wait aloiusl entirely 
'confined to liue ^=14, since it happened to be impracticable 
{without mollifying the niioronieter) to measure any other line 
both in the direct and revereetl position. Four sets of measures 
Were mnde at different times, and the following table gives the 
results. 



Ta*lb V. 


— CiniTATnRE OF 

{SayitUt fvr ys= 


RteiAt: LiKB 
5 C3-) 


^■14. 






Swlca 


t 


a 


3 


4 


DWiroD ... 


... 


■000 


•* 
- -o JO 


- ■022 


- 046 


D „ B ... 


... 


... 


-^J4 


-074 


- -ojo 


R „ D ... 


... 


-^068 


... 


4-XII4 


+ •002 


R .. K ... 




... 


... 


'(•-006 


+ *oo6 



Mmiu 



-^054 



-X)32 



-•019 



- 1017 



In thia table the " curvature" luut been measured by the dis- 
cordaiice between the midiiic of the line (represented by the mean 
of {/ K 13, 13, 14, i^, 16) und the Itnu joining Iha two ends 
(represented by thu mctuts of ;y = 4, 4^, 5, 5^, 6, and y ^ 32, 32^ 
23, 23^, 24). As tliH rL'Seaii was iiol mveri^ed in Series No. 3, 
inRirumenta] error is not eliminated from the corresponding mean. 

In examining the phuto'jrapbfd lines the treatment was some- 
what different. The aim of the iiivoaligation was to obtain tlie 
mean error of the central atrip with reference to the aretiH covered 
reBpectivety by tlie refertHice and com^inrisan stars. Kight plates 
wer<! selected (fnim the fifteen previously referred to) and measured 
according to the following scheme. It must be* rcmemU^red that 
line« I to 13 could only l>e ineaaurud with the r^seau direct, and 
tinw 15 to 27 with th^ riiseuu reversed. 



PI«M. 



Straighttuai of £iiiei on /Vm/ii, Sekmat ^ Mtaamnt. 



Date. 


HMcaii UiiM. 


FrtDM. 


Spider tine. 


t9oa 


/ . 






Oct. 20 


4, 6, 8, 10, 12, 14 


Direct 


KentHd 


.. 26 


14, 16, 18, 30, 22, 24 


Rovvnml 


DirMTt 


„ 28 


4, 6, 8, 10, 12, 14 


Direct 


DtKBt 


Nor. 10 


'4. »5. >7. '9.21. 23 


R<!v«raed 


R- 


.. 15 


14, 16, fS, ao, 22, 34 


K«v«r9ld 




• • 22 


S. 7. 9. 11, 13. 14 


Uh 




DfR, 15 


14. 15. '7. 19. ai. 33 






Jan. 8 


5. 7, 9. >'. '3. M 







^fcasuroe were made at y «■ 9}, loj 

i^i. I7i> *-^^ i^l, and also at etthoi 
2o|, 2l\. 






182 Sir W. CkriUie^ Mesrrs £ddinffion and Daicidaon, Lxvn. 

Within Ihe area cooered by the cotupariton aiars tb« 
irregularitk-B a^^^ear to be simply accidental. Tablo VL slioire 
the re«>ultA for tliie area. The ms^ns of the verUcal oolntnits ure 
iiindH zero. Tbe unallness of the horizontal means ReetiiB to sbov 
that mthio this area there is no apprecinble error of the ruling 
iiiachiiu-. The mean clL-viutiun from struightne«a (including error 
of mea)^ll^ement and accidental error ot tbe phots examined} 
is ±'024. 

The mean error of the central strip referreiJ to the Mj'iare 
g to It)* in found (from Table VI.) to be - ''•oo6±''oo5, a quantiLi 
which ia almost □egUjtiblo even for parallax. 

In the larger area occupied by tbe n/*<rence rfar» cur^-ature 
sensible. For line 14 it nmonnts tn -"'048 (nieasiired by tl 
sagitta from 5 to 23), wltii-h may be i-omparMl v-ith the reanltt fc 
the silver reseau given in Table V. The results for the oUw 
lines cannot be- jjjven separatyly, since iiiBtriunetitttl error was oul] 
eliminated from their menn. The mean curvature of all tbe eve 
liJies fromx = 4 to:r=:34 (measured in the same vrnj) ia — **oao. 



It may legitimately bn a.iked M-bpthtr, in spit*' of all pree 
tione, the error« dHtfrmirteii in the foregning invostigations anil i\ 
accuracy clainierl for the values found may not bii to aome 
illuwry. Is il i{uite certain that all in 9 tru menial erruru have' 
fliniimtted? Is it certain that there uay nut be other sources 
division error wliich have not been considerf d I Kortnnately 
discussion of the residtinla of tbe comparison and reference sian 
supplies an indcpejident rlLnck on the results obtained hy ilirect 
measurement. Itvfure the measurementx of the reseau and its 
prints were made, it was reiiliatfd that considerable corrections were 
required in ordor to reconcile the (ilaces uf tim stars di-tenuiQed 
with the teleflcope west and enfit reHpectively. The plate centre 
waa the same for all platcit taken on any one night (evening and 
Uiorning); if ou the ereuing photi:.igr!i|<hs the-imuge of a star fatU 
at *-«=i2 ;/"io, on the morninj; pholograjjlis (with the rJseao 
revei-sed) it will full at j: = 16 // ™ 18. It t-an be nhown that tiic- 
(Utference in thti places of the star di^terniined from the two seta 
phot^jjjraphs should be equtil to the sum of the residual diviaii 
errors of those two points of iho TL-seau. 

An examination of the places of tlie stars was made for 
nights on which at It^ast two plates wi^re taken with The ti*le{ 
in each position. There were 14 nighta thus available ; liie 
number of coaipari»on star>i discnsMsd was 73, and of refereotl^H 
stars 146. The compMrit^un star^ were ruferrud to the mean of t1i^| 
comparison atnra on the plate; accordingly tbe division erross 

* It will be Iran thkt the ■qoars 9 to 19 U repreimted by 1 la points evaoly 
■libtriltoteil or«r it, «»ch inouurvil on at least two printa. 





Hbd. 190/- 


0«d«i&r»r««<c/'Aa<<9r^MU/Ate«ii. 1S3 1 


^^ 


j ,5?p?s9pp8p 


M 


r 


— 


i 1 1 1 + 1 + + + + ♦ 


I 


/, j^yppM^Ps* 


^^1 




• ' ' ' ■ + + + + 


^^^^^H 


^^^H 




« .'Sgppp^pSp? 


^^^^^^^1 

^^^^^^1 


^V 




+ + + + +( 




^M i 


1 


fr J^ppl^pS^P 


^1 






+ 1 + 1 + + + - 1 


^^^^1 

^^^^H 
^^1 


^^^1 

^^H 


3 


- J?^fp^^^93 


^^H 

^^^H 


^m 


^ 


' ' + + + + 1 ' t 


^^^^1 

^^^^^B 


^^H 








^^1 






^^^H 


^^H 

^^^r 




-. -PP*p'8pS'Sg?p 


^H 


^^^" 




" ' ' + + +1 


^^H 


W ^ 






^^1 


^ « 






^^^^1 


^^H 
^^H 




— — '*»»» — — — •!** 

J. ,P P p p p p p p ^ P 




W 2 


t 1 1 1 + + 1 + + 


^^1 






^^^^1 


^^^b 

^^^F 


, .^ppS'pgMp'p' 








+ + P 1 1 1 + + 


■ 






5 -PPPPPPP??3 






+ + ' 1 r 1 + + 1 




1 








> 


y 


- .MSpP????? 


H 






t 1 1 + t (-*- + + 


^^1 








^^1 


^^ 


1* 
G 


s .°3???'p5p?g 




^^K 




1 + ' + '++ 1 




^^^H 




» -PPPPpPpppg 


Jk^^^^h^^I 


^^^H 




+ * 1 + t + + 1 , 


a^^^^^^H 


^^H 




» ,pppp3p'S5'p*p 


^^H 


§^ 


^ + 1 f + p ( 4. + + 


3 


/* "" " 



184 On the Errorx of a Pfwtogni^hed R^XLu. LXVn. 

deduced are referred to ttie square 9 to 19. The referance sti 

similarly give division errors referred to the stjuare 4 to 24. 



Vrooi 8ters 



8%tmM of Fairs of Residual Divinen Sn-ors. 

CoMpariaon Stan {/rvm y=g to y-tg), 

« B 9. 19 10, iS II, 17 tt( tA 

■ ■ * ■ 
+-04 +*oi + \j6 too 



By direct mcaiitroment 
(T.l.lr IV.) 



+ •04 



•05 + -04 



•A «S 

m 

- -lo 



•09] 



- -lal 



R^ettnee Start {fron !/ = 4 to tf<=24X 



Proiu stars 

67 iliiT^rt mrjumrcnidiit 
tdi-i1ac«d froniTnljlBlV.) 



S>*3 


?.»• 


9< 19 


• t. 17 


+ "08 


+ ■05 


+ •04 





+ •03 



•03 



-06 



+ ■04 



«*•*! 



In the IntLor table by the division error about tine 5 is meui' 
the mean tlivii^iott terror butwuen 4 uiiil 6 ; similarly for the other 
liuett. The divi^iun error bass beeo re;^ard>:>ij as iudependeut of 
80 thai all 8tai-8 betweuii the ipven liniits of x were used. 

Fifteen ciim^^arisiin nUin fait in the strip bounded by 
y= 13 and 15 j^tj and 19. After correcting their residoals for 
the revised ilivision errora which dujieod on x (Table IV.), th« 
remainiug differences (between their positions deteroiiucd from 
plates with a-Ki>aii direct and r<>ver«cd) Ahould be equal to twice 
the error of tlie strii) referred to the wholo square. In tlii« way 
we find from tlie mean of thn fifteen dtarp ttie error —'•01 ± '•oo6, 
which may he coniparoii with the direct determination (by use 
the apidcr-Une) -"'006 ±'"005. 

The prubahle error + "'006 of tlio result given aliovo 
ioferreii from the diar.ordancps imfftr « of the re«idualB for 
fifteen Ptars. The mean discordance of the«e is ±''05, wfaiob 
reprcaeats usually Meau of two plates W. ~ Mean uf two platea E., 
and the ajipurcnt corrontiou W. or E. is half tins ijuantity. 
retiulta ihut the me.tn error nf mesAurement on a i^ingle plate 
±"•05 for a tomtiariaon star. The error nf mcaaurenient for 
reference star (over the wider field) is apparently much larger. 



ST 



>o6» 

I 



Roi/n-l Obntrcatory, Grremoitli : 
1907 January it. 



Jan. 1907. Wirt-lTUervaU for a Transit InMrumeni. 185 



Note on Iht DetermineUion 0/ ike Wire-IntervaU for a Traiuit 
Imtrummt. By W. H. M. Christie. 

In Uie ordinary use of a transit inatruiuent, the transits of stars 
are observed orer the whole system of wires (^y 9 or more), and 
the instrumental errors (collimatiou in particular) are referred to 
the cuntnil win*, 8u that the vrire-tiitervals are required maiuly to 
refer the mean of the wires to the central wire with it high degree 
of accuracy. 

A ready method of dgiog this independently of star transits is 
to oompare the direct and refl^-cted images of each |>oir of wires 
(rackoned from the centre), the small a^mmetrj of each pair, 
relatively to Ibe ceotral wire, being meaJiiirt'd hy tlie micrometer. 

Thus, with a system of 9 wires, the observations would be 
arranged as follows: — 



Win-. 


Wire. 


Wire. 


Wire. 


ll> 9R 


5D 5R 


5D 5R 


9D iR 


3D SR 


5!^ 5R 


5D5R 


SD 2R 


$1* 7R 


5l>5R 


5D5R 


7l>3R 


4D 6K 


5D 5K 


5t) 5R 


61) 4R 



—the reflect^Kl image in each cai^e being brought into coincidence 
(or contact on alternate Hide.") with the direct image. 

Thus the interval between the central wire and the mean of 
the other 8 wires is determined with the full weight of eight 
observatiiins ; and a^ the tltAtiinces between the direct and reflected 
images of the pairs uf wires are very small, Che resolt is practically 
independent of errors of the micromtfter Mrrew. A nioderate 
number of determitiationH made in tliis^ way should sufhce to reduce 
complete transits to the cvntnil wire. 

Fur iucum|ik-t<; transits of <|iiick-inovin^' stars, the interval of 
each wire from the centre wire is required with an acf^iiniry whir;h 
should be several times greater than thut of a single ubscrvatiun^ 
any error in the adoptctl wire-interval being in this case accidental, 
and not syuteDiatic. A few transits of close circumpolare, or a 
very moderate number of transits of quick-moving stars, would 
amply sufHce fur this. 

For close circumpolar otars observed on wires other than ttiv 
centre wire, it would, of course, be necessary to determine the wire- 
interval from the centre wire with an accuracy i;ona' 
exceeding that of the observation; and for such casea, 1 
occur, special provision would have to be made. 

The great bulk of transits observed would be ' 
method explained above. 



Mtgat ObaervaUrrjf, Ortmvriek: 
1907 JoHuarp la 




i86 



Dr A. M. W. DounUng, 



Utvit 



7^ PUiee» of Zodiacal Stars for the Epoch 1 90a. 
By A. M. W. Downing. D.Sc, F.aS. 

Some yenrs ago the project waa formed of oon8tructiD|» 
catalogue of zodiacal ittani, frDiu all available sotirctH^, that vot 
serve, for a decaJe or so, fwr such purjjases ae the aupplj of 
sul^cit'Litly accuraW plsctrB uf a lurgs tiuuiUer of stars Uable to 
occultatioQ by the Moon, and of stars suitable as Moon-culmiiiataci. 
This catalogue (hereinafter called the Zodiacal Catalogue) wu 
published in its comploted form in 1905, as vol. viii. part iii. 
of the Antrunomicul Papers "/ the American Ephemeri* and 
Nautical Aljnxitute, uuder thu title of " Cataloitue of Zixliocal Stan 
for the Epochs 1900 and 1920, reduced to an abmluto sjatem." 
As it is fairly complete to magnitude y'o, aud contains a good 
maDy stars fainter than 7*0, the calaloj^'ue, as thus described, may 
a|>pt*ai- to be lUther an ambitious utidertukln^. Acc4']tllti^ly, I have 
been glad to avail inyaelf of the (tpportunity otIeriKl by the publica- 
tion of the Clips (rmwral Cittaliujiie for 1900 (part i. of which 
gives liiH places of 1265 of our 1607 zodiacal stars) to utiliae itfor 
the purpUi^e uf cLcckiii^ thu general accuracy of the Zodiacal 
Catalogue at the initial epoch. 

The Zodiacal Catalogue is reduced to the ayeteni of NewcomM 
Fundamental Catalogue, and coiitaiuii all the suitably placed eta 
in the latter (31 1 111 number), with their places unchaogsH. 
Gape Cataloj,'ue is also reduced to Newcomb'a Hystem, both in rii 
ascension and in lieclinatinn, and, in addition, the right ascenaioi 
are corrected for peraonuUty depending on magnitude. Aa 
Cape places are printed without inclusion of the proper mntioaft, 
have applied, iu all ca'ics, iho effects of the fjro]fL'r motions given in 
the Zodiacal Catalugue to the Cape places. Only Kome 50 stars i| 
the Zodiacal Cataloituo have no pi-opor motions assignod to them. 

It was decided to reject dilferences between thu catalogue 
amounting to, or ureater than, o''3 in right ascension and 3 il 
declination. The adoption of this criterion rasulted in the exclusiuD 
of 8 ri}{ht a.''censioiii» and 3 dfclinutLons of the Zodiacal Catalogue 
from the comparison. No Newcomb star has been excluded. A 
caae of discordamrft in the right ascension of (i Vinjinu was Crw;«^^ 
to an error in the Cape Catalogue, whore the seconds of ri|^l^| 
ascension should be 2g"'3 74, in place of 29"o82, ^™ 

The means of tho residmds wtthoul regard to sign for three bourlv 
groups of catalo'^ie differences, takmi at miidom, are then found 
tn \•^f^ •■050 and ''.15 in right ascension and de<^]ination respectively 
for the complete c(im]nirij4on, incl'iding the Kewcomb stars ; aud 
"019 and '■31 iu right ascension and decliuution fur the Newooub 
stars. 

The differences between the catalogue places have been combined 
in groups extending over one hiuir of right ascenninn. As the titan 
here dealt with are all ecliptic stars, it ia not jKuuible to separale 
discordtDces depending on right asceueion from those dupunding 00 



m 

1 




I 



Jan. 1907. Placrs 0/ Zodiacal Stars/or tiu £poeh 190a 187 

declination. The mean declination corresponding to the middle of 
cacb hour of rit^bt a9c«iiKion has accordingly been entered iu 
Tuble I. This table givea the meau differences 10 right H8ceni«ion and 
de<:ltnatioD of the Zodiaciil CntJiloguo (including the Nevcomb slant) 
mintu Cape in the columns beaded I., and the corresponding mean 
differences Newcomb mtriu»t Cape in the columnn beaded II. The 
subicnpt figurvti are th& nuiubcni of stars ui:xurritig in each group. 

As before mentioned, the Cape right ascensious are corrected 
for personality depending on nia^-nitudo. The effect of this is 
apparent in the relative values of the meau differences of the 
oolnmns 1. and II., under the hAiuling Ao. The nieaa magnitude 
of the stars discussed in column L is about 6 ; that uf the stars 
disoosoed in column II. is 4 or 4'$- As the ri^ht a-sceusiuiis uf 
stars of the fainter magnitudes Itavo n relative corrftction of the 
negative sign applied to them in the Cape Catalogue, the difference 
of the means is thus accounted for. The outstanding differencaa 
occurring in columu I. under Aa, an well as tliose under A£, must 
be ascribal to the t-ffcct of tlio presence of the fainter stars with 
proper motions of inferior ai-curacy to those of the stHfs included 
in the columns headed II. It will be remarked, however, that 
there is considerable uncertainly iu the values of the individual 
groups in the columns heitiied II., arising from the compuratively 
Roiall number of nUirs in each gnmp 

III Table If. the same gronps of differences are combined in 
pairs and arranged in order of declination, so ss to nxhibit any 
possible variation du[>ending on tliat element. Iu Table III. the 
readings of the interpolating cui-ves, drawn through the pointd 
represeutitig the ui+'an difftrence* of Table I., are given for the 
bcginniug of each hour of right ascension, and the corresponding 
degree of declination on the ecliptic. 

It appears from this discussion that (as^iuming the errors of the 
Cape places to be relalivuly ioHigtiilicant) the placet) of the Zodiacal 
Catalogue for 1900 way be relied upon to within qnite narrow 
limit« for the great majority of the stars cuntiiined therein. 
Normally, these limit') should not exceed **i in right ascenaion and 
t''$ in declination, even i[i unfavourable cases, as may lie iuferrod 
fruni the values of the means of the residuals cited above. 

But we now require the places of these stars for 1910, and 
most allow a slightly wider margin of error for that epoch, and, 
from it, up to the terminal epoch of the catalogue. The average 
variations from the Cape observations, with which they have been 
here compared, are not conspicuously more irregular, r' 
1900, for the fainter stars than fur those occurring 
Fundamental Catalogue. 




1 88 Dr A. M. W. Downing, lxvil 3, 



Table I. 

I. II. I. n. 

• • „ „ 

+ -023«, +-007,3 +'22m +'26,t 

+ 'oirw + '009b + 'I?* + "aoi 

+ -oio^p +*oiin, +'09« - "oSm 

+ •02655 +-009, -■09m +*02i 

+ -0I2„ +-004,2 +'I77!1 - "OSb 

+ -oi5b, +012^ +-05,0 --074 

+ -OI3BB --oojs +285, +-o8s 

+ 01561 +'o<2|, +-o8bi +-o7u 

+ -oogu + -007,0 - -oiu - •29,, 

+ -01940 - 'ooSio + -oi« + -03,, 

+ -02444 '°°°B + '°94B + "0*« 

+ -03547 + -008,0 +'084? +-29,, 

+ -0434, + -oios + -ii* - "oSi 

+ -02348 - 'OOSfl + ^« + "OS* 

+ 0324J -001,, +-I34, -iih 

+ '032» +-006,0 +'2i» +'"w 

+ 'OSO«i + '0060 + ■26„ - -02, 

+ "oayw - "oi?? + -os« - -ijt 

+ ■o29m - -0047 + -09,1 - -09^ 

+ *033» + -006,0 +'"^ +^w 

+ -03248 + -ooSs + '1447 + -oSs 

+ •01563 --010,0 -*0963 --16,0 

+ -01 948 - -0027 +-O9so - "I2t 

+ '03364 + -00813 +-I454 +'IIl3 

+ -025O1W + '0034211 + -lOStae + ■0!7a, 

Table 11. 

I. II. I. n. 

• ■ ■ .. „ 

+33 +"0I4llB " + ■00510 + '17118 +"O']0 

+22 + -OMiaj + "ooSaa + '13,1, + -023, 

+ 19 +-oi8b8 + -008,0 -'OSn ~'tAa 

+ 15 +-015b» +"003ao +'o5m - 'Ol^ 

+ 9 +-o2i„ +-005,7 +'I3m +""i7 

+ 3 + -02987 +-oo8aj +•!$„ +-28a 

- 3 +"038101 +-009,8 +'l3i(« +"02,( 

- 9 + ■022„ - -004,3 + -0899 - -OSi, 

- IS + "024100 - -006.J1 + -02,00 - -1451 

- 19 + "0321M + -007,8 + -»8,os + -10,8 

- 22 + -042,20 + -006,0 + -iSia, + -03,4 

- 23 + -0331,8 " *oi lu + -07119 - -1 1,4 



». 


a. 


h b 




0- I, 


+ 3' 


I- 2, 


+ 9 


2- 3. 


+ 15 


3- 4, 


+ 19 


4- 5. 


+ 22 


5-6. 


+ 23 


6-7, 


+ 23 


7-8, 


+ 22 


8-9, 


+ 19 


9-10, 


+ 15 


lO-II, 


+ 9 


11-12, 


+ 3 


12-13, 


- 3 


13-14. 


- 9 


14-15. 


-15 


15-16, 


-19 


16-17, 


-22 


17-18. 


-23 


18-19. 


-23 


19-20, 


-22 


20-21, 


-19 


21-22, 


-15 


22-23, 


- 9 


23-24. 


- 3 


Means 



Jan. 1907. Flaces of Zodiacal Stars for the Epoch 1900. 189 

Tablr III. 

I. II. I. II. 

b . « « ., „ 

0, o +'o26 + -ooS +*i7 +-13 

1, + 6 + -020 +-007 +-i8 -r-l8 

2, +12 +*Ol6 +'OIO +'IO +'o8 

3, +17 +-oi8 + X)io +'03 --01 

4, +21 +018 +'007 +04 -'04 

5, +23 +016 +-oo6 +11 - -05 

6, +23 + '016 +'004 +'i6 "oo 

7, +23 +-oi6 +-004 + -14 +*oi 

8, +21 +'015 +'oo6 +'o6 -'07 

9, +17 +'013 +'oo2 -oo - 'lO 

10, +12 + '019 - •001 + -02 'OO 

11, + 6 +'028 +'oo4 +'o8 4-'i2 

12, + o + '036 + '009 + -10 + 'lo 

13, - 6 +'033 +'oor A-'io -oo 

14, -12 +"030 'ooo +'io -'03 

15, - 17 + '033 -OCX) + -iS 'OO 

16, -21 +'039 + "002 +-22 +'02 

17, -23 +'042 -'003 +-17 --07 

18, - 23 + -037 - -008 + -lo - -08 

19, - 23 + '032 - 'ooi +'09 - •02 

20, -21 +-030 +"005 +-09 +01 

21, -17 +'023 +*OOI +-03 - 01 

22, - 12 + "020 - '003 + -02 - 'lO 
23,-6 + '024 + -002 + -09 - '02 



^1 190 


JiiV. 


T. K Espxn, Mkivmeirical Measmts 


LznL^ 


^^^ Mientmstrical Measures nf Double Stam (Fourih Ssriet). By the 


^^ 






Rev.' 


T. E, EHpin. 






^^^F Tha fttara 


mea«iired in 1 


906 have been 


mainly those of K 


^T In the liitt o 


f tht^ae 


raeaaureg which is here 


giver 


1 an aftt«riek 


H figatust the number of 


tlie gtnr denot^'a tliat tk 


\K ohjtKst observed i^ 


H not Rxactl.v in 


thni place 


! given ' 


by /t, and the difference 


is then givafl 


H in the notes. 


The followimp 


^tars 


I have uot 


8t> far succeeded nfl 


^^ idetitifyiDK : — 












■ 


^^^h 




h 


ra • 








■ 


^^H 


5455 A'8| 


f)|&ce 3 


4914 N.P.D. 


58-10 {1830) 


1906 Nnr. 13 ^H 


^^H 


339 


3 


49'S 




58- ro 


1906 


Nov. 30 ■ 


^^H 


340 


3 


56- 7 




58- 


I9CJ6 


Nor. 30 ^1 


^^H 


2593 


11 


51 54 




49 -IQ 


1906 Apii) 10, 21 H 


^^H 


2670 


>3 


3a 50 




56*16 


1906 April 9. 10 ■ 


^^H 


995 


»3 


4926 




62-17 


1906 Oct. 13. 16 1 


^^H 


B.A. 

1900. 


D«oL 


P. 


D. 


Maci. 


iMte. : 
1900 + . 


KIchu. A 


S4SO 


a 67 


+35 35 


232-6 


475 


91. '30 


687 


^^^H 


622 


20*6 


+■34 14 


131*3 


jS-22 


9-0, 9-0 


47S 


^^^H 


1032 


2G7 


+aS 58 


2463 


12*29 


8*3. ro 


6-80 


^^^^1 


62s 


30-4 


+ 39 43 


2829 


14-38 


8-9, 14-0 


671 


^^^1 


629 


5ij-| 


+ 34 ' 


|J9'3 


10 38 


8-5. II -5 


6-86 


2BC ^^1 








743 


71-26 


A= 8-5 


6-86 


a AB V 


631 


' 595 


+ 27 37 


1569 


2t '92 


8 8. ii-o 


6-90 


^^^H 


636 


1 8-8 


+ 30 


287-5 


20-57 


77. >i-o 


6-S4 


^^1 


107S 


t 18-9 


+ 27 3 


89-8 


iS-iS 


8-5. ii-S 


6-87 


2 AB ^^H 








897 


28-34 


C= lo'o 


6-87 


2 AC ^^B 


6S3 


a 37*6 


+ 30 58 


409 


22-99 


7-8. 117 


6-85 


^^^H 


328 


2 35 "9 


+ 3* 3 


245'5 


13-07 


9-5,11-0 


647 


^^^H 


329 


2 47 9 


+ 3> 18 


1060 


35 4 » 


80. 13-5 


6-S6 


^^^H 


336 


3 36'4 


+ 32 37 


316-2 


31 -es 


8-0. iro 


6-92 


3 (=E 43^^| 


670 


3 56 4 


+ 31 S3 


226-8 


10-50 


95. 95 


6'9J 


H 


349 


4 41 I 


+ 34 35 


85-6 


987 


9-1. 95 


4-98 


^1 


3S0 


4 44*6 


+ 34 37 


3081 


5 5° 


ro7, 107 


6-q6 


^^^1 


3265 


5 »*3 


+ 36 55 


i37"o 


1 4 '63 


9-0. 9-0 


6-13 


^^^1 


3266 


5 "5 


+ 36 52 


617 


8«5 


9"o, 10-5 


613 


^^^1 


^ 3*7* 


S 13 -3 


+ 39 14 


34»9 


lS-86 


77. I3-0 


609 


2 AB ^^H 


■ 






296-4 


27-31 


C= 13-3 


6'1I 


3 AO V 


r 






4*5 


32-69 


D= 11-5 


6-«3 


2 AD ^^1 


■ 7>3 


5 49 6 


+ 33 15 


2SS0 


10' to 


8'9, 9-0 


6-92 


^^^H 


■ 380 


6 a-8 


+ 34 29 


21-8 


18-67 


9'o, 90 


6-09 


^^H 


■ 3^2 


6 ao'8 


+ 38 10 


3137 


■5*89 


9-0, 12 '2 


6-04 


^^^H 


■ 3284 


639-8 


+ 36 17 


84*8 


542 


10-2, tl-2 


6-09 


^^^H 



Jan. 


907. 


9/ Zhuhl* iitan {Foh 


rth Serial). 


191 


1 


LA. 

■9CXX 

li m 
6 462 


DmL 

190a 


p. 


Dl 


MMi. 


Osta. 

900+. 


yiiAtu. 


3285 


+ i«i5 


253 * 


It'll 


9-6, 107 


6-04 




■ 757 


7 1-3 


+ 35 22 


43-8 


940 




6-ti 




7 161 


+ 34 »7 


1059 


5-28 


9-8, <o-5 


6Y19 




7 a7*S 


+ 35 5' 


1 78 10 


4-Sl 


♦ 4, 95 


6-10 




3*95 


7 3'-3 


+ 39 5 


<5S 


2275 


8*5, I0\> 


6-04 


3(3iiiSnQ.) 


3301 


7 43'8 


+ 37 28 


61 -3 


2347 


77»I37 


6-07 




3303 


7 49 "3 


+ 35 46 


31 "3 


12-05 


9'4. 11-5 


6-11 




3305 


7 54 4 


+ 37 9 


229V 


439 


9^ 9-0 


6-06 




77a 


7 55-5 


+ 35 43 


585 


12-32 


97. i3'o 


614 




4J6 


7 57 I 


+ 35 >* 


805 


I2-t8 


9-5. »»S 


6-11 




330S 


8 37 


+ 35 4fi 


2653 


46*01 


6-3, ia>9 


6-19 


a 


793 


834-3 


+ 3529 


2541 


10-25 


9-0, io*o 


6-12 




1483 


9 5*6 


+ 36 3a 


193 "9 


15*19 


9X>, lo'o 


6-1 1 




2491 


9 106 


+ 34 56 


200*4 


1421 


10*3, 10*3 


6- 10 




2493 


9 137 


+ 31 9 


157 "4 


997 


lo'i, 117 


6*t4 




462 


9 I7S 


+ 30 34 


7'5 


18-01 


9 3. 96 


6-27 




_ 463 

■ 815 

3509 


9 175 


+ 3040 


347*5 


2441 


91. «o-5 


6-27 




9 14^ 


+ 33 K> 


»44-5 


13-98 


8U 13-0 


6*24 




9 46-8 


+ 37 41 


68-5 


J4-oa 


... 


6-25 




47i 


9 499 


+ 31 9 


3»''9 


W-4S 




6-38 




3318 


9 S77 


+ 36 44 


3393 


2397 


9*1. 9*5 


6-U 




475 


10 3'i 


+ 32 6 


1724 


27*63 


67, I4X> 


6-37 


2 


253» 


10 22-5 


+ 4043 


3-6 


874 


8"9, 9'3 


6-14 


3 


353* 


10 237 


<38 29 


248*3 


12-64 


9*0. 9'o 


6*tl 


3 


4»a 


10 36*2 


+ 3* 54 


»43 4 


40-96 


6-0, 12-0 


6-27 


2 


483 


10 363 


+ 32 42 


1335 


>5'34 


8-8, 10 -b 


6-37 


2 


»555 


10577 


+ 39 7 


45 '2 


11*22 


100, 11-5 


619 


3 


493" 


10 58-2 


+ 33 as 


3^77 


17-18 


9-3, IO-8 


6*27 


3 


499 


M 22*8 


+ 36 52 


254-0 


39'59 


8-5.117 


6*23 


3 


500 


11 2fi-5 


+ 36 as 


267 


34*10 


9-1, 92 


623 


3 


■ 502 


M lii 


+ 37 35 


3 1 go 


13-42 


9-3. '2 


6-2t 


^M 


5o6> 


I' 335 


+ 39 45 


'43*5 


38-38 


7*0. 14-0 


632 


^H 


510 


J I 4S-0 


+ 38 16 


2517 


24-86 


9-6, 98 


6-28 


■ 


»44* 


12 3-1 


+ 33 »9 


33' 3 


11*55 


9*0, 100 


6-30 


1 


2600 


12 6*2 


+ 33 50 


34' "5 


lt*4l 


9*9, 10-2 


6-31 


^ V 


523 


12 471 


+ 35 '9 


183-3 


14-41 


9*1, 9-3 


627 


^ ^^^^ 


524 


13 477 


+ 33 28 


3889 


17-87 


9*3, 11-0 


6*29 


3 ^^^^ 


528 


13 lo'4 


+ 40 t6 


179 -9 


187s 


91, lO'9 


6»9 


' ^^^H 


368t 


»3 42-3 


+ 33 37 


362*9 


13*' 


11-5, (J-o 


6-28 


^^H 


587 


14 36 3 


+ 37 42 


2984 


16*32 


8 5. "5 


6*57 


^B 


»63 


14 57 9 


+ 38 2 


112-2 


1779 


9-2, 11-5 


6-60 




1340 


18 389 


+ 32 25 


822 


13'«9 


9-2, 11 -6 


657 


H 


1379 


19 9-2 


+31 38 


3070 


9*30 


9*3, 11 "a 


6'69 


1 





Rrr. 


7", ^. Eapin, Afieromelricftl Measures 


LXVIl. M 


^^^_ 


X.A. 


Uecl. 


P. 


D. 


Uac>- 


DM*. NtithU. 


■ 


^^^h 


1900. 


1900. 








1900 + . 




^H 


^^^^^^p 


h m 














^^1 


W '383 


19 15-4 


+ 31 22 


Ill -6 


ir32 


lOXI. lo-o 


6-64 


3 


^1 


■ 1390 


19 183 


+ 30 4a 


1319 


9*44 


9"3. 14^ 


6-66 


aBC{ 


ntw> ^1 


H 






100*9 


16*94 


A* 9\> 


6-66 


2 AB 


^1 


H I6t6 


2» 57 


+30 36 


293 -8 


8-58 


8*9. 97 


665 


3 


^^H 


H 1AS6 


21 40'I 


+ 3' '7 


230-2 


132S 


9*5, 10*1 


659 


a 


^^^1 


■ i6l$8- 


21 43'5 


(30 48 


3587 


14-90 


'}•$, no 


6-69 


2 


^^H 


1 i^S 


2t 44-2 


+ 30 47 


ii6'i 


13*07 


9*0, 1 1 *o 


6-69 


ft 


^^^1 


■ 1707 


21 52\} 


+ 31 28 


33' -4 


8-4i 


93. ""o 


6-6? 


2 


^^^1 


H 1722 


22 1-3 


+ 31 26 


457 


1672 


8*9. 9*9 


6-64 


2 


^^H 


I 966 


22 30-4 


f30 17 


a6«-3 


13*27 


7'o, iro 


6-68 


3 AB 


H 


H 






276*0 


3684 


C= 12-0 


6-66 


2 AC 


H 


H 972 


22 48*1 


+ 31 8 


193*9 


23-99 


8-8, lo-o 


676 


2 


^^^ 


■ '834 


" 53 '3 


+ 29 so 


165-9 


2556 




677 


a 


^^H 


^^^H 






4*3 


27-94 


C= 13-0 


6-78 


2 (new 


^^^1 


^^f 






270*3 


5821 




6-78 


3 


^^H 


V 1837 


32 547 


+ ^9 33 


349*4 


I9'u6 


8-6, 12 '2 


6-8o 


a 


^^^1 


■ '»39 


22 55-8 


+ 4035 


294^ 


13-58 


8-y, io*3 


596 


3 


^^^1 


■ 1858 


23 95 


+ 29 It 


1>4*I 


24*98 


89, III 


674 


a 


^^H 


■ 1859 


23 95 


+ 29 tS 


121*3 


3457 


7*o, 10-5 


6*74 


2 


^^^1 


^^^ 1S62 


23 'o'9 


+ 26 56 


233 '9 


16*79 


8-5, 100 


6-eii 


1 


^^1 


^H 






Furious Start. 






^^1 


^^^^H Kunis. 


R.A. 


Ucel. 


p. 


t). 


Mm^ 


Dst*. 


NV^I 


^r 




1 900. 

b. ni 

26-9 


1900. 








1900 + . 


jH 


S386 


... 


^27 57 


196-6 


42-02 


8-8, S-9 


678 


3 H 


qC&stiopeifc... 


413 


+ 57 17 


233 •« 


5-68 




6-08 


3 ■ 


Wnslibnni 6... 


1 30-2 


+ 32 31 


105-8 


2-33 


9*0. 9^ 


607 


4 fl 


B.D. +29'"33a 


I 507 


+ 29 58 


3o6'4 


S3*' 8 


8*3. 9-a 


6-86 


^1 


B.D. > 


30**303 


1 51-3 


+ 30 32 


2707 


6650 


7-6, 90 


6-89 


2 ^1 


X 187 rtj. 


1 51 -s 


+31 S 


lSo-2 


1 30s 


8-6, I to 


6-81 


s ^1 


ijTri 


^iiigiiH 


2 297 


+ 34 15 


17-1 


lj8So 


5'5. 7"o 


6-91 


^1 


2 568re.i. ... 


4 31*5 


+ 39 17 


2130 


21*50 


8x>, 11*0 


S-oa 


^m 


a594»«j. . 


4 42*S 


+ 39 5 


333 *o 


7*86 


8-5, 10 -0 


6-03 


H 


84S4 




5 22-8 


+ 33 2$ 


170-7 


5920 


... 


691 


H 


SS42 


i-ej. ... 


6 21 


+ j6 32 


180 


29-08 


8-2, 9-6 


6-SS 


H 


2 iijgrej. ... 


7 41-8 


+ 37 4' 


6-9 


'5 95 


8-6. 9*1 


6-06 


H 


a 1294 r^. ... 


8 51-1 


+33 >8 


3397 


15-01 


8-5. 9*0 


6-oS 


a ^1 


a ui* r«j. ... 


lo 3*4 


+3a 50 


3067 


35" 


9'0. 9*4 


6-oS 


1 ^1 


3 1492 r«j. ... 


10 52-1 


+31 12 


1647 


21*53 


7*8, 9 7 


6 '29 


a ^1 


2 1610 rej. ... 


12 6-6 


+ 39 21 


3305 


2893 


7*9. 9*2 


5-8' 


2 ^1 


S173 


3«j, ... 


13 16-9 


+31 ' 


1307 


12-37 


9*2, lo-o 


6-3' 


1 


X 1749 rpj. ... 


13 243 


+31 35 


350 


so'Si 


8'5, 10x1 


6-30 


1 ^1 


3 239 


5 


18 8-6 


+31 32 


1717 


9-63 


8*5, 9*0 


6*65 


a ^1 



Jan. 1907. 0/ Double Stars {FouHh Series). 



Nanaa. 


R.A. 
1900. 
h m 
.. iS l$-6 


Dm). 
1900. 


p. 


0. 


Magi. 1M«. 
1900 + . 


Nitfliu. 


A.G.a 


+ 29 s'l 


1733 


17*91 


9-0, 9*4 671 


a 


asasflwj. . 


■■ '8 347 


^3043 


391-5 


33-55 


8-8, 12-0 6*65 


1 


A.G.C. 


■ 19 57'9 


-*-il 23 


3558 


13-15 


8-3. S*9 661 


1 


H058S 


,. 30 12*9 


+ 31 12 


158 


819 


«'8, 135 6«^ 


3 \iV 








297-4 


5f34 


A- 6*5 6-64 


2 AB 


A I2l8 


.. at 19-1 


^■3o so 


22*2 


i-S7 


8'S. 97 6*5 


3 


KiistDfr 66 . 


.. 32 50'2 


+ 32 32 


»*3 


3-51 


688 


3 


5 3975rej. . 


.. 33 16 


+ 32 29 


aSS's 


29*95 


90, 9-0 6-92 


2 



A 5450 h h&B. mi ilescripttoQ. 

A 629 The only otlior ratniiureH are those of HS: — 



^J^a 



AB 

AC 



7 1 '45 
74'5 



10*93 

71*35. 



1885-83 



36 The onJj other mea^^ures are raioe :- 



287-5 30'oS an 1904*78 

h 5272 The ouly other nieaatirea are bjr /3 : — 



I 



AB 


34'7 


»9-SS 


3n 


AC 


395*0 


29-36 


9D 


AD 


437 


33*48 





1879*86 



h 493 h'a place 1" tooimall. TUerff in a third star more distant 
' ia the same direction. 

h 506 h'e d(M:. should bo iocrcaaed i". 
h 844 Not fiiunil ; »tar here given is 60 + 33**2192, preceding 

A'g phice hy 3*" lo", 
h 1390 The tQxnicjmes C is too difficult to measure satisrEctorily. 
A 1688 No star in this place. The star here given is BD + 

3o''4529, which is 2* follinriiij? A'« place. 
A 966 A's obsen'atiuu wus oiadc wh«u it was clnmlj, luid the 

primary wim i!onM.'i|u<*nt1y und^-nrnted and the third 

star miasrd. The ihird star wd- 

mnuiartKl bjr H2. Thn only xf 

those of HZ:— 




w 


'94 


Jiev. 


T. E. Sapin, New DouUe ikan. 


Lxm. 3, 


^h 


1 


New Double Stars, By Rev. 


T. E. Eapiii. 


1 


H^ 


K.D. 


R.A. 

I9CX]. 

ti m 
12*0 


DvuL 

1900, 


p. 


D. 


U«gi. Ditt*. 
I900 + . 


NlfhU B 


1 3" 


... 


+ 34 35 


237*3 


2"l5 


9-6 (0*0 6-95 


' 1 


H 313 


+3a"58 


l8'2 


■1 32 27 


i6-3 


3'95 


87 t27 695 


> 1 


B 314 


+28195 


306 


+ 28 41 


2017 


836 


8-5 140 677 


2 I 


H 315 


+ a8-ioi 


32 5 


+ 38 40 


777 


2*04 


9-1 g-4 678 


3 I 


■ 316 


+ 32't54 


47 3 


+ 32 43 


292-3 


1-92 


9*5 97 6-95 


' J 


H 317 


... 


54-9 


+ 31 56 


187-1 


659 


9*2 94 671 


' H 


H 


+ 30*823 


1 3I-0 


+ 30 55 


71*0 


272 


9-5 iiia 671 


- ■ 


H 319 


+ ii'2$6 


1 22 '9 


+ 33 2 


3907 


175 


9*3 9-8 6^5 


' H 


H 330 


+ 33*3 JO 


1 46-5 


+ 33 25 


l6['2 


r87 


85 95 6*95 


a AB^ 


B 








2598 


9*95 


C=io-o t>-^^ 


2 AC 


B 331 


+ 29-333 


I 51*6 


+ 30 5 


lSl*3 


3-63 


9-3 io*o 6-82 


2 


^H 322 


+ 32*374 


I 5g-6 


+ 32 39 


92-2 


2-32 


9*5 96 6-96 


2 


1 3>3 


+ 33'425 


2 21*9 


+ 33 39 


i79-« 


6-35 


9-1 10*3 6-96 


2 


B 334 


•«-28-44S 


2 33*2 


+ 38 28 


20-2 


I -80 


9-1 ii'o 6*97 


1 BO 


B 








185-8 


3275 


A= 9-0 6-97 


I AB 


B 335 


+ 30-465 


2 49-S 


+ 3" 10 


O'l 


13-93 


7 9 I2'5 6-94 


3 


B 336 


+31-536 


2 59-6 


+ 31 39 


361 


479 


9-8 10*8 6-91 


3BC 


■ 








35-8 


102-33 


A= 8-0 6-88 


2 AB 


1 327 


+ 32*652 


3 33*5 


+ 33 9 


392-9 


14*00 


8*3 12-0 6*95 


I 


I 338 


+ 34761 


3 47- 1 


+ 34 46 


388-4 


6-83 


8-3 1410 6-99 


3 


1 339 


+ 30*601 


3 537 


+ 30 31 


25s '9 


7-27 


90 12-5 6 94 


3 J 


B 330 


+ 3'-«34 


4 5''7 


+ 31 7 


156*1 


395 


9-2 120 6-92 


' ■ 


B 331 


+ 35*971 


4 59< 


*35 32 


324*0 


;«o 


8*6 11-0 6*93 


> ■ 


B 332 


+ 33'W7 


5 '4-8 


+ 33 '7 


210*1 


■4-65 


fi'3 8'5 6-95 


' ■ 


■ 333 


+ 31 936 


5 152 


+ 31 32 


367 


3 37 


9*2 9"3 6-92 


' V 


B 334 


S4S3 


5 21-8 


+ 33 42 


347 '9 


1509 


8y> 14-0 6'li 


2nc V 


B 








50-5 


95-48 


A^ 7*0 6-ti 


2AB(3.H 


B 335 


+3a'iot3 


S 23*9 


+ 32 34 


330'6 


3-65 


9-1 92 6-93 


1 


B 33^ 


+ 31*1027 


S 3>'o 


+ 3' 43 


258-6 


8-47 


87 90 6-92 


^ i 


B 337 


+ 3rn9i 


5 49^0 


+ 33 U 


3967 


5 -45 


9-1 12*0 6'92 


' ■ 


B 


+ 361361 


6 0-9 


+36 37 


19-5 


817 


8*5 n-5 6-94 


< 1 


B 339 


+ 321460 


654-8 


+ 32 33 


1S67 


16-40 


65 130 7-04 


' 1 


B 340 


+ 31 1491 


7 o-i 


+ 31 51 


1395 


5-63 


9*0 9*2 6*94 


' J 


■ 341 


+ 32-1522 


7 13-0 


+ 32 37 


251-6 


305 


9"0 9*0 6-95 


• ■ 


B 343 


... 


17 520 


+ 3« 21 


23S"4 


5-82 


9*0 107 6'67 


' H 


B 343 


+ 31-3133 


17 527 


+ 3' 12 


38z-8 


8-46 


9*0 1:7 6*69 


'■ 


B 344 


+ 33*2994 


17 53* 


+ 33 52 


307 


8-96 


8*6 4*1 6-63 


M 



f 


Jan. 1907. Jicp. T. E. 


Egpin, 


A'ew Double Stars. 


195 H 


^^bfo- 


B.U. 


R.A, 


DorJ. 


r. 


D. 


M««i. 


D*tc. 


^^1 


H 




lyoo. 

h in 

18 7 3 


190a; 






1900 + . 


^^H 


^■45 


+3»'3'95 


+ 31 22 


19-4 


="45 


9'1 9-3 


6*64 


^^^^1 


^B^fi 


+ ,?a'3io2 


18 J7 I 


+ 3' 10 


307-0 


6-10 


9-5 13-0 


6-58 


^^^^H 


^B47 


+ 32 '31 03 


IS 17-2 


-*-32 »7 


66-6 


175 


9-0 92 


6-62 


^^^H 


^p... 


+ 29-3420 


18 54-4 


+ 30 I 


172-3 


17-91 


9*0 9-4 


671 


^^^^H 


^^4S 


+ 2S'32IO 


19 5"o 


+ 28 15 


256-3 


5-53 


87 1 1 -3 


6-76 


^^^^^1 


349 


+313482 


19 6-8 


+ 3< 35 


220-8 


665 


9-3 130 


6-58 


^^^^H 




+ 3* 3487 


19 7-0 


+ 31 57 


2353 


5*41 


8-5 9*3 


6-58 


^^^^H 


35' 


r 33 '3398 


19 13-3 


+ 33 21 


S2-4 


615 


8*8 iix> 


6-8 r 


^^^^H 


.35^ 


+ 34' 3504 


19 17-1 


+ 34 15 


tii'o 


4*67 


8-9 lO'U 


6*Si 


^^^1 


m^' 


+ 33M5r 


19 237 


+ 33 7 


296-4 


336 


8-6 10-2 


675 


^^^1 


■354 


+ 31-3785 


>9 445 


+31 29 


324-4 


9-30 


8*6 11*5 


674 


^^^H 


3SS 


+ 3> 38'4 


I9 4«» 


+ 31 27 


2948 


13*^^5 


7*4 13^ 


6-70 


^^^1 


356 


+ 31-38(6 


19 48 3 


+ 3' ^ 


343' 


574 


8*9 9*8 


6 70 


^1 


B357 


03389 


19 487 


+ 30 52 


3065 


942 


6*5 iz'o 


6-66 


3AB ^1 


F 








I S3 -4 


[2-57 


C= 85 


6-66 


3 AC (02 389) H 


^35« 


+ 3' *i9<4 


19 S97 


+ 31 33 


197-3 


742 


8*6 10-0 


6-63 


^1 


^359 


^3' '39' 5 


19 59-8 


-31 38 


61 -t 


S7» 


li-S 13-0 


6-60 


iBC ^M 


■ 








131 U 


2791 


A= 6*5 


6*60 


^M 


■-- 


+ 30-3900 


3D 2*9 


+ 30 58 


62-3 


^7-37 


8-8 9-5 


678 


3AB ^M 


P^ 








251-2 


3340 


C= 9-3 


6-78 


^M 


; 360 


... 


20 3-5 


+ 30 48 


78-2 


274 


9*8 9*9 


6-66 


^H 


j6, 


+ 303908 


20 4-0 


+ 3023 


"3'S 


482 


9-0 ii-o 


6 -68 


^^1 


^d6z 


+ 30'40oS 


20 19-0 


+ 30 »6 


268-2 


4-48 


iro 13-2 


6-67 


^M 


P 








2294 


918 


A= 87 


667 


^^H 


^363 


+ 30-4018 


20 r9-4 


+ 30 33 


280-4 


3'05 


9*3 9-3 


671 


^^^1 


364 


+ 31*4089 


30 33 4 


+ 31 25 


377 '3 


8-47 


87 12*5 


6*66 


^^H 


,365 


+ 31-4125 


20 29*0 


+ 31 25 


288-2 


2-50 


i2-a 12*1 


6 -Si 


3 CD ^1 


^ 








262-1 


2572 


77 1 1 "5 


673 


2AB H 


F 








318-9 


33-68 




6-81 


^^B 


366 


> 30-4159 


2040-4 


+ 31 3 


I22'7 


3"29 


9-1 130 


13 69 


^^^^H 


367 


+ 29-4161 


ao 41-0 


+ 29 52 


242*5 


7-27 


91 14*0 


6-88 


^^^^H 


368 


+ 30-4180 


» 43'9 


+30 38 


3S7'9 


2-88 


9-5 9* 


6-64 


^^^^^1 


369 


-f 31 '4226 


2044-6 


+ 3' 37 


300-4 


673 


8^ 12*0 


6-69 


^^^^1 


370 


+ li'i23rj 


20 45-0 


+ 3< *6 


39-3 


s-si 


9*3 13"5 


6-8 1 


^^H 


^_37' 


+ 30 4227 


20 49 9 


+ 31 


1337 


3-67 


90 9 3 


6-66 


^^^1 


m" 


* 31 -4273 


20 52-1 


+ 31 35 


144'Z 


297 


9-1 9-4 


6*74 


^^^H 


373 




20 546 


+ 29 56 


U7 4 


2-49 


98 1 1-5 


6-69 


^^^^H 


^74 


•^3l'43'9 


ao 58-6 


+31 22 


2304 


4-5± 


II 'o 13-6 


6-81 


^^^1 


b 


^ 


_ 




1371 


24-78 


A= a-a 


6*1 S 


^^^^1 



w 


196 


Jiet: 


7*. E. &jiin, J. 


VV«; DoiiUe litanL 


uxvu. ^ 


^^^^Ko. 


B.D. 


B.A. 


Ded. 


P. 


D. 


U«K». 


Okie. 


.ftcMs. 


I 




I'JWX 

h m 

31 4-4 


19OU. 






1900 +. 




■ 375 


+ 304335 


+ 30 ii 


221-9 


4-40 


9'o 9*5 


6-64 


2 


■ 376 


+ 30-4411 


21 179 


+30 20 


2147 


1061 


8 6 127 


678 


3 


K 


+ 31-4430 


31 IS-I 


+31 13 


210-0 


3-49 


97 lo-O 


6-84 


xBC 


H 








290-8 


4938 


A= 91 


6-84 


2 AB 


V 378 


+ 31-4470 


a I 24 -7 


+ 31 5» 


2037 


774 


8*6 ii-o 


e^eo 


2 


■ 379 


f 29'4444 


31 2S'9 


+ 39 4S 


300-3 


877 


9*0 10-5 


6*73 


2 


■ 380 


+ 29-4452 


21 30-4 


+29 so 


3lo"9 


2-46 


1 1 -2 11-5 


674 


3CD 


^^K 








53-3 


»3-SS 


8*5 14-0 


679 


1 AB 


^^v 








106-9 


57-85 


... 


671 


3 AC 


381 


+ 31-4539 


21 40-5 


+31 17 


109-5 


4-89 


87 13-5 


6-S9 


H 


381 


+ 31 -4560 


31 46*6 


+ 32 n 


319*1 


10*95 


77 140 


673 


6AK 1 










320-4 


60-22 


C= 7-S 


6-81 


1 AC 1 


38J 


+ 34-4586 


21 57-0 


+ 34 43 


16S-1 


4-62 


9*2 11*6 


695 


^1 


384 


^ 3r46t2 


21 5i>-4 


+ 31 4> 


66-5 


. 2-99 


9-1 9-2 


663 


fl 


38s 


+ 32-4340 


32 2-4 


+ 34 6 


35-6 


5-17 


9X> lo'S 


6*94 


2 Ab H 










362 


33-60 


C = io-o 


6^5 


1 AC B 


3« 


+ 33*4427 


33 3-5 


+53 S 


757 


6-95 


a-6 127 


6-94 


^1 


387 


... 


22 S'O 


+ 3* 53 


268-5 


1-65 


lO-O I0-2 


6-74 


^1 


38S 


+ 3<*4653 


22 8-8 


+3' 38 


2626 


7-5S 


8-8 9*3 


6-65 


^H 


389 


+ 29-4630 


32 ll-ti 


+ J0 7 


261-7 


7-38 


9-0 10*0 


672 


^H 


390 


+ 31-4406 


22 18-2 


+3« 57 


2(12 'I 


13-98 


9'0 93 


6-75 


H 


39' 


+ 29-4687 


22 28-3 


f29 50 


347 "I 


564 


9*2 1 1 -2 


6*79 


■ 


392 


S Lioerlw 


32 31-4 


+ 39 6 


2247 
185-4 
»54'3 


936 
21-66 

28- 14 


8-8 13-2 


6-90 
6*86 
6-86 


4 w " 

1 AH IS 29; 
I BC M 
1 CD ™ 


^^^ 








"5^9 


41-67 




6-86 


W 393 


+ 30-4785 


23 38-9 


+ 30 43 


259-4 


943 


8-8 t3-<^ 


6-64 


3BC 


H 








297-5 


78*48 


A= 8*5 


6-63 


1 AB M 


1 394 


+ 29-4764 


22 42-3 


+ 30 4 


338-9 


4-57 


9-1 11 -J 


6-80 


' I 


■ 39S 


+ 29-4813 


32 51-8 


4 30 6 


35>-J 


4-05 


9*3 13*0 


671 


* I 


■ 59^ 




3Z 587 


+ 30 50 


277 


3-8i 


9-3 9 4 


6-67 


> ■ 


■ 397 


+ 3»'4598 


23 5*6 


+ 32 36 


151-8 


sss 


9-2 11*4 


6-94 


'J 


1 398 


... 


23 18-8 


+ 31 45 


264-3 


4-09 


9' J iro 


6-67 


>■ 


■ 399 


H 29-4937 


23 24- 3 


+ 29 "7 


207*1 


8-53 


93 12-0 


6*76 


'■ 


H 400 


+ 39-4938 


23 24-6 


+ 29 18 


211-3 


6*40 


9-3 99 


6-76 


'H 


1 401 


+ 29-4970 


33 3''8 


+ 30 14 


7i-;J 


I -So 


9'3 I '3 


6-92 


>■ 


^^^4« 


+ 3' "4949 


23 3r8 


+ 34 5 


88-1 


4-iS 


9-2 130 


6'9l 


■ ■ 


^^V403 


-t-30-sooi 


»3 357 


+ 3034 


294-7 


275 


92 95 


6-93 


1 




Jan. 1907. Mt T^iUt, OceiUtation 0/ Saturn by tkc Moon. 197 



357 

36s 
374 
377. 
387 
[93 




Dtacordant aiiKl9s< 

Observml, iit the first inaUiiicv, in mistake for Jt 329* 

A tine pair, nnt ^veii iii atiy doublb stir catalogue u far as I 

avare. 
South 'a measurea are : — 

*'• 30° 53' Nf D. 87"'-6o2, 1825-11. Th«-i cliniiKC is due to tlio' 
pro|>fir motion of A, wliich, according to Argelander (Bonn 
Observations, vol. viit.) is o"'2o at 202* 49', acciirdin^ ta< 
Porter o"'i9 at 180'. The measures of South and my owt 
give o"i95 at I74'*i. A. hiui two Caiut comitrti Nf and Sf. 
Closely p h 713. 
352 The second nigbfa nieatiorefi trere obtained with diftic^iilty, through 

af<»g- 
Thore Hvoms to be no notice of the eloMr corner tu the measures 

previous observers. It is a fairly easy object, even in moonlitjht.' 
JtC Angles discordant. 
Measures of BC very aiict-rtain. 
380 Angles of BC dincordant. 
A little purr N of t I'ogosi. 

The faint come*, d, wds (ietect<fd in 1S93, but has not hitherto lie«a 
mevinred. 



ObMrvatioTiK of iht Oreultaiion of Saturn inj tlie Atoon, 
1906 October 27. By John Tebbutt. 

The sky was beautifully clear and the definition good daring 
the ohsftvvation of this phenomenon, A majiiiifying jiower of 74 
diameters was employed on the S>iiicii equatorial. The follovring 
are the observed local mean times uf the dilferent pluist;£i : — 

Ring began to disapp«nr . 

Bisection of halt .... 

SimultAueoiii! d I mppea ranees uf ball 

end following udge nf ring 
Di«ai'pcarancft <if Titan . 
Bull hegan to enitTtfe 
Last contact of Imll 
Last contact of ring 

The baati of the clirouomcttT wore linudible at the disappeat- 
jince. The lira^-.H wpre thfrefure noted by turning tlit- eye instantly 
from the eyepiei-o \n the fuco of the uhronotnetor. A lar^e fraction 
of a wconii wan, dniibtlE«.>^ lost in tlii.t way, nnd the times were 
cnnsoquenlly noted rather late. The iirst contact of th'- ball \t-as 
onrortunattily missed, as it follom-d ao quickly ufV:r vb%^ of VV\<3 
ring. At the reappearsnce the chronomet«r beats w«t« a\\4\\»\ft. 



b 


n 


I 


8 


17 


.S7-3 


8 


18 


'7*3 


8 


iS 


482 


8 


20 


9"9 


9 


^Z 


39"5 


9 


34 


21-4 


9 


34 


S8'3 



198 Mean Areas ami J/eiioffraphic LatUudft of LXVii. 

anil the obsprvattona maite by eye ani! ear. It was diflScnll 
Hx tli<; exaci tinieti uf llie coiitiiuUs of ilie riug id eoiiaeqncnco of 
iU throat ollifitk-ity. A star of liiiont the eii>Iith maguituJe, which 
I t<iok to )ie Titan, liisAjipi-areii middenly, but, owing u> the otw- 
]x>wiiriiig hrillinncy of the bright limb. Its reappearance could ool 
be observed. It biicauio vieiible when two or Uiree iniDUtea of 
arc fnnii thu limb. Tbe brilliancy of the planet won, of coarse, 
very much lesa than tbiit uf cliv Moon. Thia Is ibe third oc cnllft- 
Uon of Saturn Been at this ObHerratory. 

TU Peninnla, Wi»d»or, K S. Waia: 
1906 Novtmler %y 



Mean Areas and Helioijraphu- Latitiules of Sun-spots in the 
1905, rledwcf from Photograpli? iaken at the Royal Of 
tori/, Crrvtuipich ; at Dfhra DAn ; at Kodaikdiuxl Obtert 
India; awi in JUaurititu. 

(CommunietUtd by the Aatronomer Ro^fol.) 

Tlio results here given are iti continuation of thone printed in 
the Mouihhj Noli'-t-'i, vol. Ixvi. p. 85, aud are deduced from the^ 
measure men t« nf photograpbtt tAlceri at the I^>yal Obaenratoi]^| 
Greenwich; at Dchra Dun; at the Koiiaik.^»nal ObservatoiT^^ 
India; and at the Royal .\Lfred Observatory, Mauritios. 

Table I. yives the mean daily area of umbm', whole spotA, ard 
faculie for each synodic rotation of the Sun in 1905 ; aud Table 11. 
gives the same particuturs for the entire year 1905 and the four 
preceding ye-'ir.-, for the salte of comparison. The areas are given 
in two forms ; first, projected areas ; that is to aay, as aeon am 
measured on the phoCcgrujiba, these being expressed as millionT 
of the Sun's apparent disc ; and next, areas as corrected f< 
foreehorteninp, the areas in this case bein^j exjiresaod in milliout 
of the Sun's risilile heuiiBplieit*. 

Table III. exhibits for each rotation in 1905 the mean daily 
area of the whohr spots (corrected fur foreshorleuing), aud the mean 
Leliographic latitude of the spotted area for spots north and for 
spots south of the eijuator, together with the mean heliographic 
latitude of the entire spotted area aud the mean distance from the 
equator of all sputi^ ; and Table IV. gives the same information for 
the year as a wboEe, similar results for the four preceding years 
being added, as in tho i:asi4 of Table II. 

Tables IT. and IV. are thus in contiuuuiion of the simil 
tables for the years 1874 to 1S8S on pp. 381 and 382 of vol. xli, 
of the Monthly Xotiren, and for the years 1889 to 1902 ou pp. 46; 
and 466 of vol. Ixiii., atid for the years 1901 to 1904 on pp. 86 
87 of vol, Ixvi. 

The rotations in Table 1. and Table HI. are numbered in co 
linuatiou of Carrtngtou's series (Observatit/nii 0/ Saiar Spots ma. 



en 

I 



I 



Jao. 1907. 



Sim-^tois in Uu Ytar 1905. 



199 



I 



at Sedhilt, by K. C. CarrinKtou, F.H.S.), No. i beiof,' the rotatioo 
conimeucing 1853 Nuveinber g. The nf«uraed prima meriiJian is 
that vrtiich parsed ttiruugh the ascpiuling noitu at mean noon of 
1854 January 1, and the assiimed periiKl of the Smi's hiJereal 
rolaiioD ib 25-3S days. Tlits datt-^ nf the commciu-eineut of the 
Totatioua arc given iu Graunwlch civil time, ruckoiiing from mean 
miiloight. 

Table I. 







Ko. of 

IVkjaon 
which 

Ph»t4r- 

www 
Ukflu. 


Hwn or DKlly AtwM. 


No.o( 
RoU- 

tint). 


Uat«ol 

Coiu nwBoeinvi 1 1 

iif Mvh 

B«laUon. 


Proj«et^. 


Comclod (or Fotv- 

■iMHteiilBg. 


Umbiw. 
229 


nrhok 
l6ss 


Funis. 


tTinbrv. 




3138 


686 


1905. d 
.Inn. 5-53 


38 


1987 


166 


1255 


6«7 


F«li, I "87 


27 


395 


2746 


^584 


370 


t938 


3703 


68S 


Mar. rao 


28 


229 


1992 


"J4 


'55 


•3«S 


2394 


6S9 


2:S-52 


27 


99 


6?a 


3194 


66 


421 


»333 


690 


Apr. 34'lk> 


a? 


170 


II4S 


1865 


"5 


7S3 


3009 


691 


Mny 22-03 


a? 


87 


S67 


^348 


65 


437 


2633 


692 


JUUU lS-22 


27 


222 


1523 


2309 


156 


1 123 


3533 


693 


July 15-43 


aS 


309 


Z174 


3633 


230 


1672 


2903 


694 


An;;, n'64 


J7 


181 


J300 


3057 


>30 


883 


3238 


695 


SK[.t. 7-89 


a; 


136 


916 


3476 


98 


692 


2643 


696 


Oct, 516 


38 


399 


3096 


2401 


288 


330b 


2610 


697 


Nov. I -45 


27 


365 


2607 


3009 


36j 


1939 


3'76 


698 


1B76 


27 


.90 


1204 


2707 


»33 


850 


2839 



Table II, 



Xtmr. 



190T 
190Z 
1903 
t9H 
1905 



on wlikh 
PboicoTitpb* 



3S9 
349 
3SU 

363 
364 



UnibnD, 

U 
14 
67 
93 



UmttOI nmj Atmb 



?mjMt«rf. 



I Oamctad tor far«bon«ii| 



WlMla 
SpoU. 



41 

86 

434 

S?3 

«fi37 



nuaiii. 



Dmbrw, 



33 


9 




163 


10 




875 


S» 




1639 


67 


^433 


i*3 , 



Whole 
JtpoU. 



3t 



f 










^ 




200 


Mean Areas and ffeHographie ItatUudes 


0/ Lxva 3, 








Tablx IIL 










So. of 
RiiLa- 
II (W. 


1 

So.ot 
Ween. 


Spot. NOttTII ot 
tha l£r|iiAhjr. 


S|X>U SOtiTU of 
the BqnuLor. 


Mvaa 

Bdtn- 

vt KiiUrr 

Ar*a. 


llUtMO 

olaU 




Moaa 

of 
Itairy 
Aruu- 


Ueiin 
HcUu- 

Kraphii- 
UKItuilu. 


M««n 

of 
Dally 
Aroaa- 


l<«llo> 
ltrn]>lilc 
LMllai)«. 




6i>6 


1 

1905- '1 

J»i.. 5*53 28 


594' 


Il'-SB 


661 


Ij'19 


- *'44 


t 

t3*6S 


1 


687 


Fab. 1 -87 J7 


682 


'3-37 


1256 


1675 


- 6-u 


is'syj 


688 


Mar. I '30 28 


875 


10'S2 


510 


16*48 


+ 0*58 


127^1 


689 


38-52 27 


'75 


16*42 


246 


1808 


- 371 


IT'^I 


690 


A^tr. 24-80 37 


439 


16-55 


343 


15SS 


+ 1-34 


tft-jj^l 


691 


.May 22*02 27 


2^4 


11-61 


2'3 


14-25 


- 0*99 


■'^H 


692 


Jim.- [8-22 ' 87 


68S 


9-5* 


435 


i4'47 


+ <t Ji 


ii'^H 


693 


July 15*43 < 38 


1143 


12-55 


530 


14^ 


+ 383 


■I'^l 


694 


Ang. 11-64 


a? 


638 


12*04 


Mi 


17*65 


4- 3*81 


U'^l 


695 


S»i>t ; -S9 


27 


423 


13-69 


268 


<4-38 


-t- 3-So 


'3'*^H 


696 


Oct. S''*» 


28 


2168 


11-31 


3S 


1374 


+ IO-S8 


lt*^| 


697 


No". I 45 


27 


1422 


959 


S'7 


1471 


+ 3-II 


ioi^H 


«98 


28-76 


^7 


1 4^9 


10-55 


431 


15-31 


- 2-35 


"^H 





Tablk IV. 



YMr. 


N'xof 

wbloh 
PImU- 
irapliB 
were 
takan. 


Mpou NOKi-n or spuu aovTU or 

Ui« IquAiur. tha Rquatur. 


Usui 
lltUv 

TjitHtidv 

Df Rutin 

Aruk 


^ 


Unw ot 

AXMM. 


Hello- .-,11 UpKo- 
graiJilc y^ paphlc 


1 


1901 
1903 

1903 
1904 
1905 


359 
349 
350 
3«3 
3«4 


32 

4" 
13a 

26S 
750 


8"-59 7 1^-27 
i8*bi 21 15-39 
i8-t> 2oH ai'T5 

16-33 **o '^'88 
11 6(1 440 1555 


r2'aa 

+7'4» 
-5-85 

-^»'J7 
+ 1*60 


H.-94 



'fhe itrinciiial features of the record for 1905 uro — 

I. Th« great inrreMti jn the nitoaii daily spotted area as aoin- 
pared with 1904, hoth the iiniWrx aii>l the whuLta hpyAs showing an 
a(lv:uice uf 144 pi>r cent. The nclual urea uttiined, 1191, h 
pattsvd Unit of the yuar 1S83, the year of timximum in the 
cooiplete oyole registei'ed at (jrcutivricli. 




Sun-spots in the Tear 1905. 



201 



3. This increase Ims been fairly »;eneral througbout the year, 

lu fewer thiiti »eve.a rotations in 1905 ezce(^clni({ in nreA ihe most 

liiTe rotation of 1904. Three periods 'if remarkable activity 

noticed, — the tirut thrvo months of the year, the inonth of 

Tuly, ftud the months of October and November. 

3. The faoulfe have, aa iisnal, maintained a more st«adj rate of 
advance than the spots, the mean daily are* showinj; no j?reat 
Huctuation from one rotation to another, and the whole year ehovr- 

Jiiif; ait adrance upon 1904 of only 48 per cent. 
4. Compario.!; the whole spotii of fthe two Iiemispherea, the 
northern hemispia-ro has prceorved and increased its superiority 
over th(^ noutbetn, the area for the former being to that of the 
latter aa 63 to 37. In the two preceding cycles thia proportion 
between the two liemispberes ^v-as reached about two years before 
the niHximum, the balaneo being heuvily in favour of the aoutlicru 
hemisphere by the time the maximum was reached. 

5. Notwithstanding: this smitll relative activity of the southern 
lieniispbere, usuidly much the mote disturbed ut maximum, the 
diatrihution of spoU in latitude appears to point to 1905 having 
been th<- year of niuxiimuiiL of the present cycle, since the mean 
distance from tho eqnatur of all sjiots barely oieeeded 13'. This 

K corre»pond.t very clofely to the values obtained in 1883 and 1S93, 
^ the years of maximum in the two preceiliny cycles. 

6. Whilst the 8un was nt^ver free from npots in 1904, there 
were two itayti on which this occnvrod in 1905. 

7. The dietributioji of ?pota in latitude was somewhat wider 
in 1904, every latitude from the etimitor up to 33* being 
lentcd, an arrangement usitally cboracturistic of the maximum 

'year of the cycle. 

S. The nujiiber of (ifparato groups of spot« was 355, as com- 
])arfld with 276 in the previous year. The averagp siw^ of th« 
groups was nearly double tlmt observed in 1904. Indeed, the 
most strikiii:;,' peculiiirity of the Siin-!<jKjt record in 1905 was the 
great number of abntirmnlly larjje groups; flroup No. 5441, 
seen from 1905 January 39 to ]''c^bruHry ti, attaining nn four 
consecutive dayti a greater area than that of any other spot aa yet 
included in thu Greenwich measure^. 

9. Of the 353 separate groupa, 309 were in the northern 
hemisphere and 144 in the southern. 




Jteifol Obmrrvatoiy, Oretnwi^ : 
1907 January S. 



202 



ObstnkUiom of Minor PlaruU/rom 



LIVIL 



ObservtUiotu of Minor Ptcmett from Photographt taken tcith the 
30-tnc/i Befiector of the Thomj>gon Kf/uatorial at the Roj^ 
Obaervaiory, Oremmch, during the year 1904. 

(Oammunieniai by the A3trmti>mer Reyai.) 

The fallowing positions of minnr planets were obtaiaeJ from 
photographs takes with the 30-inch Reflector during the ytMt 
1904. 

The pliites were measured with the astmgraphic micromeier. 
Four relerenre aiar« were, as a rule, measured with the planei, 
their poajtiuns being derived when possible from the Catalogues of 
the Aairoiiominclie Oeeelluctiaft. 

The positions given nro not corrected for Parallax. 

log I'aralLftx Correction = log I'arallax Factor -log A. 



1904. 


Ap(iftr*Ht UuA. 


Apparoitt IteD. 


K.A. P«. 

■ 




d 


h m ■ 


^1 ID ■ 


* » ■ 




m 








(388) CliMjbdii. 






Feb. 


■S 


11 14 15 


8 37 i3'So 
t37) 


+ 35 S 587 

Fide*. 


+8-423 


+o58« 


F«b. 


>3 


9 16 7 


8 38 15-32 


+ 23 51 43-D 


-9*271 


+ 0-646 




15 


10 ao 15 


8 36 30-84 


+ 32 54 38-3 


-8-817 


+ 0-614 




17 


iO 3» J2 


8 34 53*47 


+ 22 56 38< 


-8469 


+0-6JI 




18 


9 26 


8 34 to 21 
(106J 


+ 22 57 38-1 
Dione, 


-9-341 


+0*641 


Feb. 


8 


»o 43 15 


6 51 33*32 


+ 34 I 3-2 


-9™>a 


+o*6ll 




13 


9 40 59 


8 4; 21-28 


+ 34 '5 353 


-9217 


+o*6cx 




'5 


10 45 '5 


8 45 46-07 


4-34 ao 50-0 


- 8*605 


+o-6ot 




17 


M 14 M 


S 44 I5''S 


+ 24 25 34-7 


+ 8-448 


+0599 




iS 


9 24 5 


8 43 3478 


+ a4 37 36-0 


-9193 


+0-617 








(313) Cliildrt. 




i 


Fflb. 


'5 


10 7 58 


9 M 5»'37 


+ 1 43 1-5 


-9-210 


+0-836 




18 


9 45 S 


9 19 6-55 


+3 46 31-8 


-9'306 


+ 0'830 



(505) Cava. 
Feb. 15 7 7 9 4 59 26 "67 +25*9S7*» -8-423 +o' 



Jan. 1907. Photographs taken at Greenwich, 1904. 203 

DftteftDdO.H.T. Apparent E.A. Apparent Dec. Log. PartUlu Factor. 



"904- . 

d b m ■ h ni ■ 



rt.A. Dec. 



(454) Mathesia. 

M»r. 10 9 40 24 10 20 17-95 +'9 29 59*2 -9'i58 +0-677 

15 10 19 20 10 16 8*23 +19 35 36*0 -8'6o9 +o"665 

16 10 II 8 10 15 22'35 +19 36 8*9 -8-675 +0*665 







(334) Chicago. 






Mar. 10 


10 17 29 


ID 44 5275 +10 57 47'2 


- 9'079 


+ 0759 


16 


10 36 16 


10 41 2274 +11 21 57-5 


-8-673 


+ 0-752 



(47) Aglaja. 

Mar. 10 10 54 17 10 53 21-84 + 9 48 I5'i -8-870 +0766 

16 10 56 33 10 48 31-24 +10 9 4'9 -8-386 +0762 

21 II 21 12 10 44 43-14 +10 24 16-4 +8-728 +0*760 

(134) Sophroayue. 

Mar. 21 10 53 3 II 57 6-i6 -4 59 54 '4 

Apr. 6 10 14 22 II 41 50*68 -4 23 37 'o 

9 II 4 22 II 39 21-15 -4 '7 3'o 

12 10 33 53 II 37 5-26 -411 1-3 

(46) Heatia. 



- 9-025 


+0-862 


-8-635 


+0-860 


+ 8-771 


+0-860 


+8-505 


+ 0859 



Apr, 


6 


10 44 2 


II 47 


34*42 +1 28 10-5 


-7 '903 


+ 0827 




9 


II 35 41 


II 45 


22*72 +1 44 27-8 


+ 8*984 


+ 0-826 




12 


II 24 


11 43 


21*85 +' 59 28-1 
(19) Fortuna. 


+ 8804 


+ 0-824 


Apr. 


9 


12 6 


II 54 


36*68 -0 30 15*1 


+ 9*082 


+ 0-839 




12 


II 27 


11 52 


27-80 -0 14 18*3 
(288) Glaake. 


+ 8-955 


+ 0*837 


Apr. 


15 


10 46 36 


I* 43 


47 '46 +3 30 597 


-8-565 


+ 0-813 




18 


9 47 51 


12 41 


50-39 -f3 41 49"6 


-9-031 


+ 0-813 




21 


II 18 59 


la 39 


58-55 +3 5' 5'2 


+ 8-771 


+ o-8ii 



(403) Cyane. 
Apr. 15 II 20 34 12 55 19*51 -16 56 23-3 -00 -vo-qw 



204 ObservatioTis of Minor Plaiiets from LXvn. 3, 

App&reiit R.A. Apparent Dm. Im. P 



Date and O.M.T. 
11)04. 



PuaUuKMtar. 
Dee. 



h m B 



Apr. 15 II 55 2 
18 10 13 20 



Aiir. 15 12 24 4 

18 10 52 17 

M»y 3 9 52 26 



h 111 a 



(317) Roxaiie. 

" 57 59 '69 -34654*9 +8708 +0-857 

12 55 20-35 -3 29 '8-2 -8-948 +0-855 



(47S) Terneate. 

13 9 2-07 -iS 27 77 

13 ^ 55'9' - '** 2 50-2 
12 57 43-24 - 15 56 i8'o 



(121) Heriiiione, 

May iS 10 28 59 IS 39 42-22 - 15 49 46-7 

19 10 25 36 15 38 56-63 -15 48 37'6 

31 10 26 44 15 30 0-93 - 15 36 33-1 

June 3 10 39 31 15 27 54'95 -'5 34 i6'5 



+ 8913 +0-914 
-8*687 +0*914 
-8-521 +0-908 



-9*144 +0902 

-9-140 +0-903 

-8-650 +0-907 

-7-220 +0-907 







(90) Autio[>e. 






May 18 


10 59 36 


15 4S 12-92 


-19 13 5-0 


-9*029 


+0-914 


19 


11 3 26 


IS 47 22-69 


-19 II 9-4 


-8-972 


+ 0-915 


3' 


" 13 51 


IS 37 29-78 

(79) Eur 


-18 48 13-6 
■ynoiiiu. 


+ 8-306 


+ 0-917 


May iS 


II 31 28 


16 10 S'24 


-16 5; 139 


-8-951 


+0-909 


19 


II 48 16 


16 9 10-23 


-16.51 14-S 


-8726 


+ 0-911 


3' 


10 52 42 


15 57 40-4S 


- 16 5 26-7 


-8-68i ' 


+ 0-908 


June 3 


II 36 22 


15 54 51-46 


-"5 54 37'3 


+ 8-682 


+0-908 



May 18 12 5 30 



Jiiiie 3 12 8 10 



(153) Hilda. 
16 9 8-83 - 18 19 396 

{176) Idutrna. 
16 34 24-59 +25 38*3 



-8-527 +0-915 



+ 8-546 +0-823 







(322) 


Plifeo. 






June 20 


II 44 54 


17 41 49-22 


- 20 25 32-9 


-7 '533 


+ 0-913 


July 5 


12 I 37 


17 27 56-92 


- 19 37 49"2 


+ 9-163 


+ 0*912 


6 


10 55 49 


17 27 9-34 


- 19 34 58-4 


+ 8-660 


+0*918 


8 


II 2 37 


17 25 32-43 


- 19 29 8-1 


+ 8-860 


+01917 



Jan. 1907. Photoglyphs taktn at Greenwich, 1904. 


H 




AppateBt R.A. Afipu^it D««. 


Los. PKnllax Factor. ^^^H 
Dm. ^^^I 


d 


h m • 


(317) Bndon. 




■ 


Jvlf 6 


" 54 JS 


17 39 55-8' - 5 32 37^ 


+ 9"06» 


+0-865 ^1 


S 


II 48 36 


>7 38 37"I3 -5 41 4>'6 


+ 9-078 


+0-865 H 


9 


13 39 54 


'7 37 58 3» 5 46 4^3 


f 9-271 


+0-863 H 


IJ 

1 


ti 6 18 


17 36 4«-8i -5 56 45-6 
(419) AunliA. 


+ 8-875 


+ 0-S68 H 


JuDe 18 


II 29 32 


'S 34 1955 - '7 39 i2'3 


-9108 


+0*909 ^H 


30 


13 14 47 


iS 32 46-38 17 33 S9-8 


-8-585 


+0-913 H 


July 1 


»' 3 37 


18 33 5946 - 17 II 37-8 


-8-844 


f 0*911 ^M 


6 


13 14 5 


18 30 4'20 - 17 4 46*8 
(364) litra. 


+ 893S 


+ o'9io ^H 


Jolf 6 


13 ri 46 


20 16 9'54 -21 a6 193 


-81013 


+0*914 H 


a 


13 M 17 


20 14 19*33 - 31 3S 37'8 


+ 8*014 


+0*924 ^M 


b " 


II 3S 33 


20 7 33*58 - 22 21 30*6 


8*974 


+ 0-933 ^M 


1 " 


u 51 35 


ZO 3 1*39 -33 53 31*6 


-8-469 


H 


L 


11 II 35 


^ 5775 '^ 58 21*0 
(483) SeppiDA. 


- 8*95* 


+0*934 H 


Jnly 20 


13 31 "S 


30 44 4644 +3 15 51*3 


+ 8*804 


4-0'833 ^^H 


Aug. 2 


II 20 3 


20 36 I9'55 + 1 10 8'9 


-8707 


+0839 ^M 


1 ' 


II 9 36 


so 33 41*31 +044 477 


-8-583 


+0-833 ^M 


l» 


10 38 36 


30 32 34'3I 4-0 31 39*0 

(US) Thyri. 


-8-863 


H 


5RJ 3 


n 52 49 


«> 54 15 72 - 16 46 59' 


- 8 477 


^^^H 


8 


II 18 4 


30 47 17 32 - >6 37 37*3 


8 564 


+0-910 ^M 


13 


10 18 34 


20 43 44-03 - 16 30 so'6 


-9009 


+0-907 ^M 


17 


10 36 53 


30 37 13*10 - ifi 31 27-3 
{51 1) DaviiU. 


-8-667 


+0-909 ^^^H 


Jnljr 30 


13 t 12 


30 31 49'86 ' 24 24 S-5 
(539) P^mina. 


+ 8*586 


+(■ I ^^^^H 


Aug. 8 


II 55 39 


31 20 9*94 -6 55 :;7- 


■^; 


^^1 


13 


11 738 


31 16 3639 - 6 s-j 




^^H 


k. 


11 7 37 


21 13 8*46 7 6 ,, 


to 


_ ^ 



+8*351 


+0-865 


-9050 


+0-866 


-8784 


+0-870 


-8-383 


+0-8; I 


+ 8-356 


+ 0-887 


-9"*™^ 


+ 0-881 


-9 125 


+ 0-883 


-8-897 


+ 0-885 


-9177 


+0-833 


-9-I03 


+ 0-835 


-8-721 


+ 083* 


- 9054 


+ 0-839 



206 Ohaffrvai%(mA of Minor PlaneU from LXVIL 3. 

Date Mid O.U.T. Appanat R.A. Appwoit Dm. Lof. PualUi Vkete. 

I904- B.A. Dae 

d hma hmi a • u 

(236) HonorU. 
Aug. 8 12 22 17 31 17 22-40 -5 20 3-0 
12 10 40 55 21 14 22-18 -5 44 14*6 

17 10 48 II 21 10 35-02 -6 17 35*6 

18 II 739 2! 9 50- II -62435-4 

(372) Palms. 
Aug. 18 12 39 15 22 13 16*96 - 10 6 21-7 
Sept. 3 9 26 32 21 37 43-84 - 9 56 22'2 

7 9 23 33 21 53 58-20 - 9 53 io'9 
9 9 48 48 21 52 8-02 - 9 51 21-3 

(389) ladiutria. 

Sept. 3 9 48 54 22 15 5424 +0 27 27-5 

7 9 46 18 22 12 29-S9 +0 II 8-5 

9 10 24 o 22 10 49-87 +0 2 34-0 

16 9 12 17 22 5 32-92 -o 27 35-0 

(95) Arethiisa. 

Sept, 7 10 14 o 22 23 46-92 +11 33 29-2 -9-006 +0753 

9 10 50 35 22 22 18-94 +11 21 46*8 -8-442 +0-752 

12 II 8 59 22 20 i2'5i +1! 3 11-3 +8-388 +0-754 

(284) Amalia. 

Sept. 3 II 4 12 23 23 o-ii +!! 38 25-2 -9"I46 -1-0-755 

7 10 47 I 23 1940-24 +11 928-9 -9'i36 +0759 
9 II 47 9 23 17 56*45 +10 53 3-4 -8-415 +0-755 

16 9 45 9 23 12 1147 + 9 50 59-4 -9'2i6 +0772 

(33') Ethcridgea. 
Sept. 9 12 12 13 23 16 30-46 -10 58 33-5 +8253 +0-891 
Oct. 3 9 14 12 225844-98 - 11 43 26-S -8-957 +0-892 

(405) Thia. 

Sept. 19 9 19 4S 23 50 26-78 +16 58 5-5 -9'384 +0-725 

20 iQ 12 45 234933-81 +1652 90 -9*205 +0-708 

Oct. 3 7 53 >** 233855-46 +152625-8 -9"423 +0745 

8 9 34 25 23 35 8-40 +14 48 35-9 -8930 +0721 
12 94610 233224-11 +1417561 -8-559 +0723 



HSan. 1907. J'hoUignejfhs taken at Greemeich, 1904. 


1 


H OMvudO.M.T. 


Aitpuwtt il.A, ApDorwt Dec. 


Log. Fvftllu Vtatar. ^^H 
Dm. ^^^H 






(373) MoltMina. 




^H 


^BSept. 19 


10 36 16 


I a7-4i -a 53 233 


-9-I5* 


^1 


mocu 


9 50 34 


33 4S 1873 2 42 33** 


-9"036 


^M 


B 


to 7 27 


23 44 I -02 -2 36 7 2 


-8*650 


^M 


^L 


10 10 58 


23 40 5274 - 2 29 33-8 
(238) Tycho. 


-7-981 


+ ^M 


S«ptl6 


10 II s 


23 59 »79 + 14 4 »70 


-9-398 


H 


. 


9*3' 


^3 57 >5S5 +'3 27 367 


-9-429 


^M 


I '° 


9 57 25 


23 56 3738 *^^i U 7*4 


9-381 


H 


h 


1043 


»3 52 19-9S +11 36 48*9 
(375) VnaU. 


-8-863 


+0750 ^M 


»tpt 19 


9 42 ti 


1 5920 +11 33 33*8 


-9347 


+0766 H 


30 


10 31 30 


1 3*27 +ii 33 i7"4 


-9164 


•I-0-756 H 


Col. 3 


8 26 10 


23 49 so'S? +11 ao i7*3 


-9-369 


+0769 H 


8 


10 32 5 


''3 45 5''9 '*'" >> *9'^ 
<37o) UodwtiM. 


-7-814 


1 


OoL 3 


10 y> S7 


as 11*04 +»8 39 30'5 


-9*OJ4 


f 0-683 ^M 


8 


10 57 55 


20 23-36 +iS II 5-2 


-8-372 


-«- 0-681 H 


12 


II 4 57 


16 45^5 ^'7 45 T<> 


+ 8-304 


+0-6S6 H 


'3 


JO 1 31 


15 5476 +17 38 37"S 
(68) Leto. 


-8-884 


+0-690 ^1 


Sept. 16 


11 4S "6 


1 7 57X)i -3 13 55*3 


-9-190 


-4-0-848 H 


<9 


10 55 S3 


I 5 46-97 - 3 20 3S'5 


-9'309 


+0-847 H 


so 


10 51 3 


1 5 0*96 - 3 M 49*0 


-9309 


+ 0-847 ^1 


a? 


II 5 3' 


59 10-98 - 3 37 53-8 


-9138 


J- 0-850 ^1 


Oct. 3 


10 sS 42 


53 4749 » 48 477 


-9-011 


+ 0-853 ^H 


Not. 3 

1 


948 35 


30 1977 -» J3467 
(482) PclniM. J 


m 


^0-851 ^^H 


WOct. 3 


II 19 $4 


49 I-9J -D c 




V 


1 


10 iS 10 


42 (0-63 -0 1 
(447) Vftl«aliu» 




i 


HoeC 13 


11 33 lO 


4)* 38-96 - 1 jb 




^^H 


L 


•1 45 59 


©47 4i'85 ' 4 ' 


^ 


^,j 



2o8 ObservtUiom of Minor Plmiets at Greenwich. lxtil 3, 

Apparent Dec. 



Date and O.M.T. 
1904. 
d h m b 



Oct. 14 II 5 10 



Apparent &.A. 
h m I > J ., 

(546) Herodios. 
o 57 1471 +3 S3 53'3 



Log. Fanllftx Factoc. 
B.A. Dec 



-8-505 +0-8II 







(335) Roberta. 






KOT. 12 


9 53 56 


2 21 38-28 +5 50 34-0 


-8-986 


+0798 


14 


9 48 59 


2 19 56-89 +5 43 427 
(17) Thetis. 


-8-957 


+0799 


KOT. 12 


9 29 


2 21 42-55 +4 54 36-3 


-9-129 


+ 0-806 


14 


9 25 14 


2 19 5971 +4 48 53-5 


-9-104 


+ o«o6 



Not. 12 10 53 51 
14 10 54 13 



(170) Maria. 
2 32 2958 +38 55 55-8 -8-393 +0-275 
2 30 22-26 +38 41 29-8 -7-612 +0-3S3 



Not. 14 II 22 22 



(178) Beliaana. 
2 27 5-87 +14 9 55*4 



+ 8-693 +0725 



Dec. 5 
7 


10 26 8 
8 55 47 


(298) Baptistina. 
3 13 40-46 +27 17 9'6 
3 " 47"93 +27 10 446 


+ 8-255 
-9099 


+ 0553 
+ 0-569 


Dea 5 

7 


10 58 53 
9 26 48 


(443) Photographica. 
3 19 5619 +11 30 35-4 
3 18 19-53 +n 25 26-4 


+ 8767 
-8-881 


+ 0751 
+ 0752 



Nov. 14 II 49 48 



(154) Bertha. 
4 36 5473 +37 17 59'6 



-9158 +0-360 



Jan. 1907. 



OccuUations of Stai's by the Moon,. 



209 



o 



I 






v: m 









1 !l 



g N N n n 
ao - - - - 

• *- J3 * * ^ ■* 



. Be, CC 



CjJ ^' OQ gj CO 05 

< O W ^ &:' S: 



[C CQ 



OQ' S ^ 

-s' a^ K 



'V^H xr\ \n tr\ \n tn 
"1 "O -O -O "O "O 



ui in tn \0 >0 >0 



>0 QO u^ 'O 






ca 



CQ O 



•O r» — — •- 



n H H n H >. H 



vnu-iiriQOQOQ 



5 .1 



__ e „ 



C 
: I 

_ D 






■"T a 

r 1 1 

« O CO 



- 3 

1 3 



I I = 

"22 

5 Oa » 



-a -S 



■< OQ 



w ■«] o 



^ : 

W - -S 

■S I 5 

I ' t 

fP -^ J5 

&- « -"l 



•3 
■c 

ll 



- w ^ 



^ 



— « 



- O 2 






S .a 



•* * Tf O 



(o '*' f^ "^ "^ 



•^ 



r^rnr^V^»-,(^r^,^[^ 



2 1 o Occultations of Stars by t/te Mooii, made at LXVIJ. 3, 













a-3 



= = :| 



aa n 



©29 

^0 "O "1 



- 228 &888S'88a8S'S'8K'8ff 



g I 



3 



CD OS 3 



I -111 

3 « — 3 o 

J3 I I ja ^ 

a pass 

[^ [3 ,jC3 J5 

- « 9 iS. 



II 



a 



a. S 



p -« -> 



O O t» m •< cc 



.11 


1 

- R 


■ "^ 3 


A 


11^ 


r$r 


5 S .2 


« 


3 3 -g. 


a 


^^ 1 


- -c 


u B u 


s 


5 •«} 


OQ 



1.1 

3 ' 3 

^ il 

-< o ■< 



s 










■0 


t^ 




E 


>o 


>o 


.0 




t^ 











^ 


^ 


" 




- 


a - 




*^^ 


1.4 


■-H 


1.4 




30 


* 


'C 


■c 


> 


> 


>- 


■J- 


-■ 


"" 


u 


u 




^^ 




3 


+ 


+ 


a 




a 

IS 




H 
3 

£ 


^ 
% 




Q 


ol 





a- - 



s 



1 sa 


■c 

3 






= : : 


= : : : 



r<ll*)fntO'*mvO*0>0« 



C 

a. 



<4 M M ft n 



fan, 1907. tfu Boyal Observatory, Gfnenimch, 1906 



si ^ aS ^ 

a* K ^ & 










2|2 LntUiuU of the Hoyal Observatory^ Edmbv.rgk. LX^'U. 5, 




TV Latituife of the. Royal Qhmrt^itvry, JCdinhuryfi. 
(CMRMMiiteUed Ay Profe»»or P. /f". OtfWH,) 

The ladtU'le of the Royal Obsenatury, Eclinlmrgh, ia gtr«ii 
in the Sauti'-aJ Afmnuof- an 55" 55' 2S'"o. This prorinonal 
value wflfi derived iumi uii oWcrvation uf a Caaiofteue in the 
priiim verticil Ky LJr liecker on 1889 (.lutobur 8. 

Fntiu 1898 A[>rit ti> the prettent time nbservatioiis have twea 
mude of Sir David (liU'a list of Zndiacal Siara. The ob»ervati(ini> 
as far us 1906 tVliniiiry havu hwu rcduceU in the firel inatance — 

(i) With au assumed latitude, 55' 55' 3o'o. 
(li) Uti&scrs Htifracliuny. 
(iii) No coneciion for 6exure. 

Comparitton oF the reuniting detilinatioiis huM b<>ea made with 
NewRuJub's Kundamental Cfltalngiie, and with the Zodiacal Cata- 
logue puhlisbed in rhn Papers i)f the AiDfricmi F.pbemeris, voL vl 
pt. 3, which is aUo rfduced to Newcomb'a aystem. 

TUu roitulij of ihia compariaoii aro shown in the first foar 
columDB of tlie following tabb'. 'I'iie observaliuus are very ffcaotj' 
fnmi the pole to Z.l). 30° S., but are plentiful from Z.J-). jo' to 70'. 

The differences, when the observations are correctetl to the 
Pulkowa l>ya^em of refractions, are given in column 5. 

The observations of flexure made between 1S98 April i; and 
ii>o6 Keliruary are as follows: — 



Omut. 


Hcrr. I'lexura. 


ftatn. 


liar. Flcxw* 


1H98 April 1} 


* 


1905 Felmuiy 23 


+o*SS 




+ i-ia 


April 15 


+ 1-03 




+098 




+ rx7 




+o-8o 


April 19 


+ 0*89 


1902 S«plmDlK-r 16 


*»53 




-fO^O 


I9>'i3 Au^^t 24 


+ i'ia 


NoTumber 7 


+ 0-84 


1903 AugOftt a; 


Mean 


+ l"lO 




+ 1-14 







4 



The ohftervattons during the year 1906 have given a somewhat 
sttialliT value. I have Laken the correction for fluxure, in round 
figures, as - I'oo siu Z.D. When this correition in applied tlie 
dilferencita from Newi-omb are those of the last i^olumu uf tha 
following table : — 




Jan. 1907. Latitude of the Royal GbserccUory, Sdinhmrgk. 213 



I 



Contparifon 0/ (he Dedinaiiona observed at the Royal Observatory, 
Edinburglty 189S-1905, mth Ifewconih'M Fundamental Sy«tem. 



Dec. 


Z.D. 


Number 
atOba. 


Nawc- 
Ob*. Dwtu. 


Rttfnctiana}. 


Z.D. 


N-0 (PulkowA 

RcfiL riatiirt 
OofrMltoiO. 


+ 9li 


-36 


*3 


-0'53 


-0-43 


-•59 


+ •17 


Hi 


-33 


19 


-0"o6 


■f 0'04 


-■54 


+ ■58 


59 


- 3i 


»7 


-0-13 


-o-ia 


-■06 


-■oG 


47 


+ 8i 


9 


-0-24 


-0-27 


+ •15 


--42 


3?1 


+ 18 


8 


+ 017 


+o*io 


+ ■31 


- ■»! 


32S 


+ 23 


34 


+0-37 


+o*w> 


+ •39 


- '19 


371 


+ 28 


2It 


+0-36 


+ 0*28 


+ •47 


- 19 


aal 


+ 33 


685 


+0-57 


+0-47 


+ •54 


-07 


174 


+ 38 


566 


+077 


+0-65 


4-62 


+ •03 


I2| 


+45 


360 


+ I-I2 


+097 


+ ■68 


+ 29 


7i 


+ 48 


37<S 


+ 0-86 


+078 


+ 74 


+ ^ 


n 


+ 53 


260 


-1-09 


+0-87 


+ •80 


+ •07 


- si 


+ 5S 


3»5 


+ I-I4 


■fo-89 


+ ■85 


+ •04 


- 7i 


+63 


418 


+ i*ai 


+090 


+ •89 


+ *01 


I2i 


+ 68 


297 


+ 1*44 


+ i'05 


+ ■93 


+ 'ia 


-I7i 


+ 73 


495 


t-i-43 


+096 


+ -96 


00 


-3J4 


+78 


196 


+ 1-28 


+068 


+ •98 


-■30 


-a^ 


+83 


8t 


+ 0-93 


+o-ia 


+ ^ 


-77 



Consideration of these rcaiiJualii shows that the latitude may 
be talcoD aa 55* 55' 3o"'o. The olwervationa from -34^' to 
+ 34^°, though few, givi) this n;sulL whatever corrt-ction be ajiplied 
for llyxure. The oliservations from Z.D. + 34^" to Z.D. 73° 
support the aflupted correction for lloxura. At the zenith dis- 
tances 78' to 82* there is a marked discartlatice. but the observa- 
tions at higher teniih dititanccs support thu chaiigi; from Eetrsul's 
to the Pulkowa refractions. 

The reduction of the ohfte^y^ia^^nJlich form the material on 
which this UetcrmioaUon of Jl^^^^B^^ hm^ed have been ac- 
celerated, thanks to a graatH^^^^^^^Btatfit Grant Committee 
of tho Royal Society. 



.'J I 



MONTHLY NOTICES 



OP TBI 



ROYAL ASTRONOMICAL SOCIETY 



Vol. LXVIt 



FxBRUABT S, 1907. 



No. 4. 



L 



ANNUAL GENERAL MEETING. 

Mr W. U. >1aw, Pbbsidsst, in the Chair. 

The B«pOTt of the Auditors of the Treasurer's accouuta for 
the year 1906 was read, and is given on p. 220. 

The Anntial Report of the Council was partly read ; see 
pp. 317 to 299. 

The Address was delirered by the President, after which tlis 
Gold Medal was hHudtrd to tho Secrotary fur trausitnsi«iou to 
Profeasor Ernest Wiltiam Brown, to whom the Medal had been 
awarded for bi:> retfvarcbes in tho Lttuar Thvur; (we p|). 300 lu 315). 

The President having appointed the Scrutineers, the Sooietj 
proceeded to the ballot for OfficerR and Council for the ensiling 
year. The namvs of those elected are given on p. 314. 

The thanks of the Meeting were k>^cu to the retiring Ofhcers, 
and also to the Auditors oi the Trcaearer'a accounts and to tho 
Scratineers of the ballot. 

Edgar T. Adams, 5 Warkworth Street, Cambridge, and the 

Cottage, TIal8t«ad, Essex, 
BobertJocckhf!ere,Observatoire Stella, Roul>aix<Nord), France, 
John Stewart, Chief Officer, H.M.S. "Kmpreas of Ch' 

The Willows, Wallasey, Birkenhead, and 
Samuel Veovora, Normanton, Kimberley Drive, Gi 

near Liverpool, 



I 



L 



«dre balloted, for and duly elected Follows of the Soc 



2i6 Report of the CouTusil to the LXTn. 4, 

The foUowiDg Candidates were proposed for election as Fellows 
of the Society, the names of the proposers from personal knowledge 
being appended : — 

Arthur Neville Brown, M.A., Schoolmaster, Ludgrove, New 
Barnet, Herts (proposed by CoL E. E. Markwick) ; 

Harry Cooper, 1 9 Cromer Road, Eastville, Bristol (proposed by 
W. F. Denning) ; 

Phanindratal Gangooly, M.A., Premchand Boychand Student, 
University of Calcutta (proposed by Aautosh. Mukho- 
padhyay) ; and 

William Newsam McClean, 42 Durdham Park, Bristol (pro- 
posed by Sir David Gill). 



Feb. 1907. Biffhty-seveTith AnvMcd General Meeting. 217 



Report op thb Council to thb Eiohtt-seventh Annual 
General Mbetino of the Society. 

The following table shows the progress and present state of 
the Society: — 



■ 


a 
2 

K 


1! 


Fellows 


m 

s 


1 


& 

o 
■a 

a 
a 

a 
1 


e 

If 


1905 December 30 


I 


2 


259 398 


49 


709 


Since elected 




+ I 


+ 2 . + 33 ! +« 




Deceased 






-5-9 


- 2 




Kesigned 








- 6 






Bemorals 






+ 4 


- 4 






Expelled 


I 


3 


... - 3 ... 


721 


1906 December 31 


260 


409 


48 



218 



JUport of the Council to tfte LXVii. 

Major HilW Account at Tre-Murcr of the\Rc 



RECEIVED. 
Balanctts, 1905 December 3I :— 

At Bniikoni', u per pMa-book 

Cbequei not crediud till 1906 

In hatid nf AKKisUiit Aecrrbiry on Aocount of 

Tumor nmi Hwrrwx Ftiml 

In band or AsiistAnt Secreu.>7 on Fett; Cash 

AMonnt 

Diridends : — 

£1,250 Metropolitan 3-per.o?nt. Stock 

£932 19 a Metropolitikn z^-pcr-cetit. Stock „, 

Hair-j't'Br's Oividond ua .£[.484 17 5 SwaniM 

Corporalidii jj-jirr-t'eiit. Stock 
Hftir-y«ar'B Dividcud on £1,384 17 5 SwaniMtn 

Corpomtioo jj-per-cent. Stook 

£3f4cx} East Indian Railiray 3-per-oeiiL Da- 

buDtur« Stock 

£3,aoa Txtndon md North -Weatern Railway 

3-per-cBiit. tX'beiitun; Stock 
£4,000 Miillftud KailffAy 3i-peT-c«tit Dtibec- 

Lure Slock 

£500 Lancashire and Yorki«hJr« Hallway j-per- 

Mtit. Consolidated Prpforcnce Stock 
£l,S6o Qaa Ligbt and Cok« Co. S-|)«r-ceDt. 

Delwtituro Stock 

£1,650 Commercial Gaa Co. j-pftr-cant. Deben- 

tun Stock 

Raooired on aooount of SubHcriptiona : — 

Arroara 

Annua) Con tri bat ions for 1906 

„ ,c in advanca 

Adtniasion Fees 

FiratCoDtributiona 

Compoaltion Fei-t 

Sales of Publicationit, kc. :— 

At Williitiiia fc Nor^te'H, 1905 

At Society's Kooiui, 1906 

Salenuf Phuto^-Apba, 1906 

locoRie T&x refunded by Comniwionem of Inland 

KeVtfDue 

Bequest of tbu Into Rbt. A. S. Farrar 

Sale of £932 19 o MotropoiiUn aj-pw-ccnt. Stock 

AodiCed and found correct, 1907 Jan. 8 : 
G. J. ^BVBKOIIt. 
A. E. OOHRADT. 
W. W, B»Y«IT. 



£ M. d. 



£ M. d. 



299 
7 18 


2 
5 






J 


4 "3 


II 




i 


1 


8 19 


10 


330 


la 


* 






35 12 
22 3 


8 

4 








34 13 


9 








26 7 











96 18 


Q 








91 4 











95 











•4 5 











53 


t 








47 «> 


6 


S06 


4 




laS 2 
596 5 

13 12 

73 'o 

52 10 









863 
87 


1 

a 
3 


1 




II 16 
94 
35 " 




8 
6 


141 


i 

9 


J 

> 






36 
100 
719 


10 


9 


6 

Q 
1 






3.7«S4 


11 


■ 



Feb. 1907. £ufhty-aetenih AnntuU Cftneral Meeting. 219 

Astronomical Society, from 1906 January i to December 31. 

PAID. 

£ t. d. £ «. rf. 

AwBtAiit Secretary : SftUty 25a o o 

„ „ Editing Society's PablicAtious 50 o o 

Clerk's flaluy , ... 75 o o 

House Duty 

Fire Itunnnc* 

PriDting, kc : — 

Meiiivirs, vol. Iri. (Spottinroode k Co.) 

MviUhiy N<4ieeA, „ „ 

ZoIipM Beuori, 1905 (IlarrUon k Sons) 

List of Fellows uid MiMX-lliiueous (Spottiswoode 

*Co.) 

Photo-tilocks ill Annual Report 

Compntktion of Ephemeriitei in Monthly ifoiieu ... 
Tamor and Horrox Fund, purchase of books (or 

Lilirary 

Reproductioa of Photognplis, Biiiton k Co. 
OaUdogniDj; utronamioal literature for the loter- 

nAtioQiJ Ostalogue of Sciratiiic Lit«mtBr« ... 

Ezpensiea of Meetlngi 

Laiit«rti eiiw>Q3teB 

TlraeStsnu: z«iit«t of wtn 

PostAjEt* tnd Telof^ams 

CarriagL' uf Pan.'els 

Stationer)* (Si'Otliawoodek Co.) 

Sundry Sutionery «nd Office expeniteM 

llliiininatiDgAildres8(BeDJamui P'rinklinCeotenary} 
House ei]t«iiBe& : Alloweuce nuil tiUUil;y expcuMs 

Ccul and QnA 

EleotrJc Lighting 

Fittings and Repairs 

Sundries 

Poraha-M) of £100 Swansea Corporation 3|-per-i:ent, 

Stock (iDvestnent of Bequest of tli« late Rnw. 

A. S. Famr) 

Purchnse of £y}<i, 1$ 3 Bwanaea Corporation 

34'P**'wt' Stock 

Pttw«r of Attorney for aali 

oent.SttH-k 
Bankers' de>iuctiotii "" 
Kei«yii)eiit of fitoo I- 
Oheqnm outsUn : 
Bilanci.-s, 1906 ( ^^^^^^^^ 

At HankeiB >» ^^^^^^^^^B 14 1 o 

Jti I'f Ami's ^^^^^^^^ 

Tumor and B<>. ^^^^^^^^^^ 6 o. 

In hand of AHla'" 
Aocoanl ^^^^^^^^^ 

19 A 





— 


375 





2 12 


6 






9 9 


6 


13 2 




649 19 


3 





376 16 





1 


M 


»7 3 





1 


I 


as 4 









14 


9 










1069 17 













'5 









12 7 


11 






35 4 


2 






30 





16 to 









8 12 









5 





30 It 


A 






V 


79 9 


6 






u 13 

4 '7 


t 






5 <o 


7 








"^ 


104 10 


1 1 


) 




3 8 





59 


7 






42 8 


3 






18 14 


10 






13 8 


7 






4 10 


9 








^~ 


137 3 









tos 16 









395 









II 


6 






*> 3 









401 12 


7 






16 19 


6 



i'2,764 tl w 



220 



BepoH of the CouTunl to ike 



LXVIL 4. 



Report of the Auditors. 

We have examinwl the Treasurer'a acwmnte of rereiptA and 
expeoditnrfl for the year 1906, aiid have found and certihed the 
flame to t>c correct. Ttie co-sh in hand on December 31, 1906, ID- 
cludiiig the balnacg ut the bankers', etc., amounted to X19, 4J1. 5(f. 

The overdraft of £400 at the bank has been repaid, but it has 
been found necessary to sell £932. i9«- Metropolitan s^-per-ciaiL 
Stock, whifih realised X719, 9*. yd. 

£379, 158. id. Swansea Corporatiou 3|-per-cenL Stock hv 
been purchmtud, in addition to the iiivesttucut of a bequest of 
£100 from the late Iter. A. S. Farrar, received daring the year. 
The result ha^ been that the expenditure for the year has exoeoded 
the income by about £200, chiefly in consequence of the Urgfi 
amount of the biLlH fur priutiug. In this coniioction we are glad 
to find that a change of printers has taken place, which we trust 
will result in a contiderablo reduction of this it»m. 

The books, instrument.<4, and other effects in the poaaeoBion id 
the Society have been examined, and Ihey appear to be in a 
satisfactory condition, witli the exception of some of the ius 
tuents in the basenietit, with regard to which we regret to &01 
that 80 far no practical result has followed from the recouimeDda-. 
tion made by the Auditors last year to eliminate those of oo 
practical value or historic iutorast. Wo desire to repeat this 
rccommendutiou with greater emphasis, as it is a matter which 
obviously grows more premising each y^ar. 

We have laid on the table a list of the namee of iliHitf 
Fu]Iuw:> who are in arrear for auma due ut the last Annual 
General Meeting of the Society, with the amount due against each 
Fellow's name. 

(Signed) 



QodH 
id».fl 



1907 Januarj/ 1 1. 



Walter W. BBYajrr. 
(I. J. NswiiEaiN. 

A. E. CONRADT. 



Jieqna4« to the General Funds of the .Srw-fVyy. 

7%« Cmringion Btqueet (1876): A sum c' 
Sold in 1899, and stands now in £1,881 
Korth-Westeru Railway j-por-eont. Del)eni' 

27i« McClean lUiiuffi ( 1905) : A fivim of £2,ocl 
sum invested in the purchase of £1,484 : , 
Corporation 3^per-cent. Stock. 

The FarroT Bequest (1906) ; A sum of £100. lovi^i. 
Corporation 3^percent. Stock. 



Feb. 1907. £ighty-9eventh Annual General Meetitig. 221 



Trust Fumlt. 

TIte Tunvtr Fund : A sum of X464 r8«. East Indi&n Railway 
3-per-c«nt Debenture Stock: the int«reat to be used in tim 
purcbuBc of books for Uie Libniry. 

The Horroz Metaorial Fund : A »utn of £103 6*. East Indian 
Railway 3-i«T-cetit. Dt-benturB Slock; the iiittreat to be uKcd 
in the pnrelKise of books for tbe Library. 

The L^f and Jaitufm FutuI: A num of £334 lOi'. gd. Ka«t 
Indian Railway 3-iJer-ceiit. Debeutiire Siock ; the interest to 
l>e Kiven by tbe Council to tlie widow or orphan of any 
de<-*(t8ed Fellow of the Society who may i^tand in need of it, 

Thfi IJannnd Jark*>in (rtA? (iirilt) Futui: A »iim of X309 i8«. 6d. 
EiiBt Indian Railwuy 3-per-cent. I>ebentU[x' Stock ; the 
interest to I>e ^iven in Meibils or other iiwarde, in acoonlance 
with the terui8 of the TriiBt. 



Anet9 and Present Prop«Hi/ 0/ the Soeieiy, 1907 January i, 

BfttanefA, 190$ Deoember 31 : — 

£ i. d. £ s. d, 

AtlUnkera' 14 i o 

In huid of Auifltatit Svcrcury ou Aecouotof 

Tumor anil HoiTOz Fiiod 460 

In haml Qf As-fiiUnt SecreUry nn I'ettjr Caali 

Account o 17 5 



Dae on sccoDot of Subacriptione : — 

LA CvntributJoiiB of 5 yt^Ara' sunJing 
I - * ■• 



42 





67 4 





56 14 





138 12 





136 





430 10 





13 12 






19 4 5 



PI. ". 

* Korgaiv for mtm of Publications, 



417 iS o 
o 15 o 

44 >S I 



.^r-tu-nt. lir)mnlat» Stock, lu- 
ll. Mi<rr»x M«morial KiUid, tht- 
I ■-■n»h JkcltMiD (nAOwiU) 

(^3, 4iB^ lUiJvn* j-pcr-wnt 1>B> 

tl. „ , • -. 
C50 



^^H 322 Heptni of the CouT%eii to tlu UE^^H 


^^^^ £1,250 MotrfipaUUn 3-]«r-ceiit. Stock. 


1 


^1 £1,864 ] 2«, 7d. Swansea Oorponttot) 3)-per-oeiit. Stork (iDoliid- ^M 
^^^ iii^£i,Soaof the McCli-«n nKjoeat of j^s.ooo). ^^^| 


^^^^ £100 SwftDHM Corporation jj-wr-cent. Stock (being 
^^^B of Oauon Furar*!! B«iu«tt). 


; InrntmeDt ^^^H 


^^^f Aitronumicftl aoil i.4tii;r Maniuionpts, Books, PrinU, Pfaoto- ^^^^| 


H Furniture, kc. 


^^^1 


H Stock or PabH{»tioDB or the Society. 


H 


^^^^^B ObWio/ Phvlograpfu. 


■ 


^T Tlie following h a list of rcpruductioiisof Ci:lc6tial Photognpiu 
H publiahed by the Kojal Astronomical Society for sale to ***^ 
m Fellows :— ^| 


H B.A.S. 

■ Rcf. Subject. 


FboUjgniihed by H 


^^^^ i Totfti SoUr Efliiiu. 18S9 Jatnury i 


W. H. Pickcriug H 


^^^H 3 Tot«) Solar EuUpw, 11^95 A^i-il 16 


J. VL Schmeberia ^^^ 


^^^H 3 Total SoUr £cHp«, 1S86 Aagunt 29 


A. Scbniter ^^^| 


^^^H 4 Nflbvls in the PMadu 


IsaAc Boberta ^^H 


^^H s Nebuk H 74 PisHun (S.G.C 62S) 


lauoRolierta H 


^^^^H 6 Great NubiilK Id Orioa 


laosr Roberta ^| 


^^^H 7 UQky Way iie«r M 1 1 


E. S. Barnard H 


^^^H S Jihlky Way near Cluster id Ftrmta 


£. ¥.. Uamanl ^| 


^^H 9 Comflt c 189J IV. (Brooka), 1893 Ootobtr 21 


K. E. Baruaril H 


^^ 10 Comet '(( 1892 1. (Swift), 1892 April 7 


E. E. Barnard H 


] t Nebula about ij ^rfrur 


David Gill I 


13 Portion of Moon (HyRintu-Albaief^niiu] 


1jo«w7 and I^iiaeiu H 


13 Comet •: 1893 IV. (Brooks], 1893 October ai 


R. e. Barnard fl 


14 Coinot f. 1S93 IV. (Brookn), 1S93 Oototer 20 


R. E. Barnard H 


15 CAmet e 1893 IV. (Bmokti], [S93 Novomber 10 


E. R. Banianl H 


16 Comet a 1892 1. (Swift), 1892 Apri] 26 


E. E. Bamuil H 


17 Ooniet/1892 III. (Uolines), 1S92 Korembw lo 


£. E. Barnard H 


18 Comet a 1892 I. (Swift), 1S92 April 18 


£. E. Barnard ■ 


19 PcrrtioQ of Moon fAl|>«, Aputtninea, Ac.} 


Loewy and Pniaecuc ^| 


30 Nvbui» i» Aniiromai't 


I«aac Roberts ^| 


31 Jupitfr, 1&92 Si'pt«mbi.<r 26 


Lick Obaomtary ^| 


22 Closter M 13 HrratliM fN.t3.C. 6305) 


W. R. Wtlun H 


33 Total SoUr Ecliiise, 1893 April 16 (5 see,) 


J. Kuaniey ^| 


24 Tut«1 Sulnr EaU|>HC, 1893 April 16 (20 avc.) 


J, Keamry ^| 


25 The Moou (Age 7** },^) 


Lick Ubaerratoijr ^| 


26 The Moon (Age 12^ 6^^) 


Lick Ob<ierratOTy ^| 



p 

1 


Feb. 1907. Highty-sevtnth Anmtal Oeneral Mteting. 223 ^| 


1 




fhtHKi^^il^ ^^H 


w 


27 


The Mood {Aga 16^ iS^] 


Uek Obaervatory ^^^H 




28 


The Moon (A«« Zi"* 8*) 


Lielc Obaervatory ^^^H 




29 


The Sun. 1892 Febru»rf 13 


Koy. Obt. Greeowiok ^^^H 


i 


30 


Thn Sun, 1892 July 8 


fidy. Obs. Greenwich ^^^H 


1 


3< 


Portion of Moou <R«!gion of Magiuiu) 


IfOewy and Pnisfux ^^^^H 


1 


32 


Tb« &I00Q (Aac u' I**} 


tJek Obwrvatorr ^^^^H 


1 


33 


PortiOD or Moon ( Ptol«nueiut, kc.) 


Lick Observatory T^^^f 


1 


34 


PortJon or Moon (Mare Serenitatia) 


Lick Obaerrttory ^^^H 




35 


Portion oX Moon (Clarini, LioetDt, ka.) 


Lick Ol'Miratorj ^^^^| 




36 


Purtton orMoon (Regiomontsniu, &e.) 


Lick Obtertratory ^^^^^^^ 




37 


Portico of Moon (Tvcbo, Tbebit. Ac ) 


Liok Obwtrvatory ^^^^^^^B 




38 


Portion of Moou (Theophilus, Ac ) 


Liok Ol>9«rv«tory ^^^^| 




39 


Total Solar EcIipM, 1896 Au^at 9 (j »eo.) 


Koatiniky ^^^| 




40 


Total Solai Eclii>««, 1896 Auf^ust 9 (36 sec) 


A. Hudty ^^H 




41 


Cluiter M 56 Lyra (N.G.C. 6779) 


^^H 




4* 


Kcbal« M 81, 82 Vrne Mnjoris (N.U.C. 3031, 


^^H 




43 


Cliiitw M 56 L}frtv (oiilargeil) (N.G.C. 6779) 


^^H 




44 


Solar Corona, 1871 Deeeialjer 12, Baikul 


H. Davii ^^^B 




45 


Solar Corona, 1875 April 6, Siatn 


Lockyer nod Sehuitar ^^^| 




46 


Solar Corona, 1878 July 29, Wyoming 


Harkoeaa ^^^| 




47 


Solar Corona, 1882 M»y 17, Egypt 


Abney and Schurtar ^^^^B 




48 


Solar Coroua. 1S83 May 6, Caroline lalatitl 


l^wntiofl and Wooda ^^^^| 




49 


SularCorQiM,iS85Septeniber9, Wi-lliiigtoii,N.Z. Radfonl ^^^H 




50 


Solar Corona, 1686 Augiut 29, Grei)A<la, W. 1. 


A. Scbiutor ^^^^1 




5» 


Solar Oorona, 1887 Auiptat 19, Jajiaig 


^^^^1 




52 


Solar CoronK, 1889 January l, Califoroia 


H. ^^1 


1 


53 


Solar CoToiia, 18S9 Docember 2z, Cayenne 


Scbaaberle ^^H 


54 


Solar Corou", 1893 April :6, Fuiidiuin 


^^^^H 




55 


Solar Corona, 1893 April 16, BruJl 


Taylor ^^^| 




56 


Oreat Nebula in Orimt 


^^H 




57 


numb-1>a1l NebuU, Vnlp^^hx (N.G.C. 6853) 


^^1 


1 


58 


Spiral Ni^iiiiia, Canax r0jui<in(N.(>.C. 5194-5) 


W. E. Wilson ^^B 


59 


Ditto (onlwrged) (N.0.0. 5194) 


W. £. Wilson ^^H 




60 


Annalar NflbuU, Lyra (N.G.C. 6720) 


^^1 




61 


MttoorTrailaittiCoinHBroaVs, i893NoTeniberi 


lUi-nard ^^^1 


1 


6a 


Total So)ar Eclipw, 1898 Janiury 32 [$ aer.) 


W. H. .M. Chrialio ^^H 


«3 


Total Solar Kclipw, 1898 Jauuury 22 (20 sec] 


W. H. M. ChrisUfl fl^| 




64 


Solar Corona, 1896 Aagaac 9, Noraya Zeralya 


G. BadocfPowell ^^^| 




65 


Solar Corona, 189S Janoary 32, Pnlgaon, India 


E. n. niiu ^ 


1 


66 

L 


Nebula in Andromida 


Roy, Oba., OrcetnH 



^K 


lUport of the Council to the LXTn;H 




1. 

snbjBot. 


FlkoCOigraphed bj 


^B 


SiifctillMi cifSun'a Llinb. 189S JuDQ&rjr 22 


E. n. iinu H 


^^H 


Annual Nclnila, Lijra (N.G.C. 6720) 


Ltek Observatury ^| 


^H 


Dttiub-bi-U Nebula, Vntp^mlni'^.G.C.iAsi) 


Lick OlMierraUtry ^M 


^^H 


Spird K«buU, Canev Vtnatiei (N'.U.C. 5194-5} Liok OltservnCory H 


^^H 


Sliiml Ni'l'ula, Ursa Major (N.G.C. 545?) 


Lick ObstTVatory H 


^^H 


Trilid Nvbulfc, S^itt'triua (N.O.C. 6514) 


Link Observatory H 


^^1 


Gnat NebuU in Orion 


Liok 0)>Mm-atory fl 


^^H 


Cliinter M 13 ^•rrtrw/it (X.O.C. £205} 


Lick ObMrratoTj* H 


^^1 


Siiliir StirTMiR wiUi Fw iilw, 1893 Aupist 7 


G. E. Hale H 


^H 


Fnculir utitl Friiriiiiiiiiii.-i.*N, 1S92J11EIV35 


0. E. Halo " 


^^M. 


ToUl Solar Eetipso, rSyS Jan. 23 (| spb.) 


W. H. M. Christie 


^H 


N^'l.ulft H V, (4 CVy" (N-O.C. 6992) 


W. B. WiUon M 


^^H 


Portion oj" Moon (TLeo|4iilui!, kn,) 


Yeikcs Obstsrvatory ^| 


^^H 


Total Solsr E^1i[MB, igno May 28 (joaeo.) 


B. B. Baroard H 


^^H 


Cottitt 1901 I., 1901 May 4 


Rov. 0)w..Cflp«orG.R 


^^1 


Comet 190J 1., 1901 Uay 6 


Roy. ObK., Cai>«ofa.lL 


^H 


Cotnot rgoi I., 1901 &U>- 9 


PtfrthOb8.,W. Atuuilia 


^H 


Sular Surfifne u-itti Fju]iil:a>, 189; Aufjiiist 18 


H. l>«8lam)K« ^H 


^H 


Solar Proiiiiii'*iin.'j*, 1S94 Aiiril il 


H. Deklaoilras ^| 


^^H 


Nebula frboat Nova Persei, 1901 SvpUimber 30 


< G. W. Kitcher 1 


^H 


Nelmla *bout Nova i'eraei, 1901 November 13 


G. W. Hitobvy H 


^^H 


ToUl Sniar EoUjiie, 1901 Mny iS (10 »oc) 


F. W. Pyaou H 


^H 


Total Solar EclijiHe, 1901 May IK (40 aee.) 


F. W. Dyaoii H 


^^H 


OoriH't b 1902 III. (IVrrino), 1902 Sept. 29 


Koy. Ol>«.. QrMnwiolfl 


^^H 


t'ortion of Moon (Mare Scienitatia, &c) 


Yerk«» OlMMTst^^^l 


^^H 


Portion of M»oii (Roii^h Oratur Region, 


4iH 


^^H 


Mnre Nubiiiin) 


Ycrk«fl Obaervatn^^^l 


^^H 


Portion oTMoou {Tycho, Theophiliu, Ac.) 


Yerken Observatory 1 


^^1 


PuKiou or Moon (Biillialdiu to Copernicus) 


Yarktw Obsvrvatovr H 


^H 


Portian of Mtinn (CojioriLicttis, i-iilargr-il) 


YerkwB Obaorvatory 


^H 


Ci-eat NcbuU ill ijriiyik 


Yerkci Oburratory 


^^1 


Ureat Nebula in Orion (Cciitml portion) 


Yi-rkf* ObiCTTatory 


^H 


Nobula io Awlrofneiia 


Yerkea Obanrvatory 


^^1 


N*buU in Cijfuu* (N.G.C. 6960) 


Yarkt^s QlMerratory 


^^^V 


Nebula in Ci/tfnua (N.O.C 6992] 


YerkM Obderratory 


^^^P lOI 


Cluster M 13 BerviUis (N.G.C. 6205) 


Yerkea Obaemtory ^ 


^^^1 


Cluster M 15 I'tgasi (N.G.C. 7078) 


Yerkaa Obwnratory H 


^^M i(>3 


Solar Surfaw witli Farulic 


Yerkes Obsenritocy ^| 


^^^H 


TLd Mooti, 1900 April 5 


P. Pitiwux ^^^M 


^^^^ 105 


Ttie Moon, 1902 Novenilxn' 13 


PoUeox ^^H 



Jeb 


1907. J?i^U]MevriaA AnmtuU Otntnl MmOu^. 235 B 


K.AA 


^^M 




■■*••*■ 


FlMtacnitedlrf ^^^| 


io6 


Tbv Moon, 1903 Pcbnuuy 6 


F. PsiMU ^^H 


107 


Tb« Uoon, 190J Sei'teuber I3 


F.PUfaMZ ^^H 


308 


KaVoJodty ^bout 15 Uan-aatUia 


K. Barnard ^^^| 


109 


Milky Way about 3 Cy^ 


R. Barnard ^^H 


110 


NcboIoaitT OMT ■ C^vjrni 


E. E. Baniatd ^^^| 


III 


llilky Wfty n«ar x Ctfyni 


G. E. Barnard ^M 


112 


Star Clnud in Sofittariiu 


E. E. Bamanl ^^^^ 


V^ 


MUky Way in tVjM^u 


K. £. Barnaid ^^^H 


114 


Milky Way about U S 


E. E. Barnard ^^^^ 


"5 


Uilky Way about OpAiueAi 


E. E. Barnard ^^^| 


116 


Milky Way near N.O.C. 6475 


E. E. Barnard ^^^B 


i'7 


Great Nebula near p Ophiutki 


K E. Bamaid V 


118 


Milky Way about 5S Ophiucht 


E. E. Barnard ^^^^ 


119 


Milky Wiiy near Omeya uvbula 


E. Barnanl ^^^| 


120 


Star Ctond in Satfiaariu3 


E. E. Uamard ^^^^H 


121 


Nftbala about r ScorpU 


E. E. Banwrd ^^H 


133 


Sun, 1905 January 30 


Roy. Ob*., HrWDWicl* ^^^^ 


123 


Sun-spot, 1905 Junnary jo 


Roy. Ola., Grwiiwich ^^^H 


124 


San, 1905 January 31 


Roy. Obs., Greenwich ^^^H 


"5 


Sun-spot, 1905 January 31 


Roy. Ola., GT«ciawi«h ^^^H 


|I26 


Suii, 1905 February 2 


Roy. Obo., Grt>i-nwiob ^H 


■ 127 


Sun-xpot, 1905 February 3 


Roy. tllis., OnwnwiiJi ^^^^^ 


P 128 


Snn, 1905 February 3 


Ray. Obm , Omtuwloli ^^^H 


129 


Sun-spot, 19D5 February 3 


Boy> Obn., flrtn'tiwich ^H 


130 


Sun, 1905 February 3 


Roy. Oba., Orfunwlcli ^^^H 


I3» 


San-Hpat, 1905 February $ 


Roy. Oha., Orevnwidi ^^^H 


13a 


Son, 1905 PVbronry 8 


Roy. ObH., On^nwich ^^^H 


>33 


SuD-spot, 1905 February H 


Hoy. Oba., Gnenwioh «^^^^^H 


134 


2febitU near i MriJmti, 1905 January 8 


Woir j^^^H 


135 


' K«bola M 33 Trianffuti (N.G.C. 598) 


Imuc Roberta ^^^^^^^M 


136 


Nebula in Penetu (K.Q.C. 1499) 


Imoo Roborta ^^^^^^^1 


137 


NebnU In M^norxrOt (N.O.C. 2237-9) 


!■■■(! Bulwria ^^^^1 


»38 


K«buta 9 V. 24 Coma (fi.O.C 4565) 


(aaac Roberta 


139 

■ >40 
141 


N«bnl« V V. 42, kc., Gmue {S.GX. 4631) 


taaac Roberta 


X»bul)i- If T. 37 Cpiriti (N.O.C, ToooT) 


lauc Robefta 


Nebnia Imlra Cat. 40S /*«»«< 


Uaai: Roberta 


143 


Clnatrr« lit ftrtevM (N'.O.C. 869, S84) 


laoar R"beTU h 


MS 


Clitator V VI. 30 CamifptUt (S.Q.O. 7789) 


iMir buhcrta ^^^^^^H 


144 


EclipM, 1905 Augaat 30 <5 MO.] 


Chi ^^^^1 


U5 


EclipM, 1905 ADffoai JO (ao mo.) 


H. CI ^^^^H 



226 



Ji^Ktrt of the Council to the 



LXVlt4. 



EtilipAe, 1905 Atigu-st 30 (7 »9c.) 
Eclipw, 1905 August 30 (20 Mc) 
EcUpse, 1905 Augoit 30 (PoTtioD) 
RejOOt> of Ntbulii p Oyhiitehi 
NebaU I* Qphinchi (ealarged) 
Hegton of 9 Ofhixtchi 
GrMt Bift near 9 OpMuehi 
GrAftt Star Cloud iu SayUlnri%ta 
SdwU SUr Ctoiiil in SagMariwx 
Rdgioo of Cluster U 1 1 



W. H. U. ChriitiB 
W. H. M. Cbrutu 
W. H. U. Cbristie 
E. E. Bftrnard 
E. E. Bamud 
£. E. Barnud 
E. E. Bunuil 
E. E. Baruard 
E. E. Baraud 
R. E. Bamaxil 



Nos.44-55, Nor. 64, 65, and No. 147 form « series of 
phatugrapliB, oriented aitd reduced to the Hame ncal«. 

Tlte above phologmpba are now du gala to Fcllowa aa prim 
either |)latinotyp>(; ur aristoty^ic, mounted ou sunk cut-out nurao' 
measuriug 12 inches by 10 inchea ; also uumounled, and as luitern 
slides. Nor. 44-55 And No&. 64 And 65 are also supplied a 
LranaitftrencieB, 6J inches square. 

Price of prints, mounted 15. 6fi. eacb, unmounted ia Meb; 
lantern (tlides, i<<. each ; packing and postage oxtra. 

Transpareucies, 6^ inches square (Nus. 44-55 and Nos. G4 ind 
65), 3ft. 6'/. each. 

Orders to be addreased to W. H- Wesley, Burlington House. 
London, W. In ordering priiitii or alidus the R.A.S. Raferenoe 
Nn. only need be ipic^ted, but in the case of prints it should faa, 
stated whether pLarinotyjieR ur aristotypes are required 
whether mounted or unmounted. 




77te Gold Medai. 

The Council have Mivarded the Society'fl Gold Medal to 
Professor Ernest W. Brown, F.R.S., for his researcheit in tEit 
Lunar Tlieory. Tiie Preeiidetit, in Ins Addreiw to the Society, givoa 
the grounds upon which the award has been founded. 



During the 
been issued. 



ViMicatitms 0/ the Society. 
past year toI. Ixvi. nf the Monthly jVi 




Vol. Ivi. of Mtrrwirs has been published : — 

Thonios I^wjs, Measuri.-B of the Double Stars contained in 
the Mmsntts Afkrometrirrp of K. (i. W. Stmve, collect 
and discussed : with an Introduction containing |^n< 
deductions, a liHt of proper motions of 6fty faint atat 
and various other information iu respect to double star 



Tob. 1907. StghtyseverUh Annual Otn&ral Meeting. 227 

The Ko;aI Society have decided to terminate the arrangement 

ider which the Koyul Astronomical Society has been permitted 

hare reprintA of astronomical papers from the i*rof4«dingB and 

^fiiiosophuai Tranaaetumf. This decision, however, does not 

relate to KclipHe reporta ; and the RoiMrts to the Joint Meeting of 

10 two Socielies on 1905 October 19 (repriuted frum the 

ling$) has been issued to Kellows a» a separate publication. 

following paper, reprinted from the Phiioaopkicai TrantactmUf 

rill shortly be iaened as an Appendix to the Memoire:- — 

F. W. Dyson, Determination of vrave-lenf;:th from spectra 
obtained at tlie total solar ecHpses of 1900, 1901, and 1905. 




238 



Report of the Council to 




OfilTCART. 

The Cotinoil regret that they have to record the lose by d(?«tli 
of the follciwing Fallows and Associate? daring ^e past year :— 

Fellows : — Rapbael Lciuis I^Uchoffshetai. 
Rev. John Bone. 

Everard Home RobortB Colomnn.'* 
Thotnim R. DalhneyKr. 
Robert Isaac: Finaemore. 
Josopli H. Frofmaii. 
Joseph (^ledliili. 
Charles Jasper Joiy.* 
John Jnynsoii. 
AUr(^d Edwunl Xicbolli. 
Roliert Rawsoii. 
VVilliAm Julin IteyiiuMs. 
Philip E. Sewell. 
Rbv. George Veiiables. 
Associates : — Samuel Pierpont LaiiKJoy. 

Jean Abraham Chri^tien Oudemnns. 



Obittiory notices are aleo given of the following, who died in 
Jauuary igo; ; — 

Agnes Mary Gierke {Honorary Member). 

William Johnston. 
William Simms. 



I 

■an, 

I 



BAniAEL LouiB BiscHoFFaRRiM, son of Louis Biscboffsheti 
founder of the Biflnhoffshcini Rank, was born at AtUBterdsn, 
33nd July 1823. At an early agi? he waa sent to Paris, there 
study fur entr)' to the Central School of Arts and Manufactu 
into which he was admitteil in 1339. On leaving the school 
was attached to the rstaff of the Railway de la Haut4?-ItaUe 
Inspe<;ting Engineer. Later, he took ovor the direction of 
father's hank, finally settling down in l^aris, where, on a4th A^'ril 
1S80, he obtained full letters nf nutnralisation for '* serriov 
reiidererl to the country." For mnny years he was well kDowQ 
for his liberality towards anything tending to promote tho welfan 
of liberatnre, science, and art, and the value of his donations wu 
fLiially arkiiowlcdged by hU adiuissioti, as life uiember, to Uie 
Acod(5mie des Scietices on i6lh June 1890. _ 

Especially fond of astronotry, he prc^sented a costly equiptni 

* Obituary in Aunual EUport, I905. 



Teb. 1907. /Sigkty-sewnth Annual General Meetimj. 239 

the Paris Observatory, the Equatorial Coufl^ and a. Maridiait 
Jirclfi bein^ due to his munificencii ; he ^ubsidisefl tlie Observatoty 
»n Mont Blanc, iind contributed lowarda the expense of redetermtn- 
ig the length of un urc uf the meridiau at Quitu. 

But he will, above all, be recnemb^n-d hs the founder of the ■ 
>beervatory of Nice, in the organisation of which he was aasiated 
>y the experieiice'and autbDrity of the Bureau dca Longitudes. 
laving brought into existence thiA f^rRat inatitutinu, he entrusted 
its din^ction to the able and energetic astronomer Ferrotin. He 
jBuerously endowed the fibservatory, and tiiially assured its future 
presenting it to the University of Paris. This foundation has 
^ndered the name of Bisctv^ffsheim faiuitiar to aatrononiers in 
Bvery land, and the Annales of hia Observatory will form the 
[imperishable iimruorial of its funnder. 

M. BiBchoffsheinj was elected a Fellow of the Koyal Astro- 
Inomical .Society on the 14th January t88i. g. b. 

Tre Rsv. John Bone was the second son uf John and Mary 
Bone, of Meltou Lodge, Surrey. He was born on aoUi Octobar 
1834. He graduated at King's T'ollege, London, in theolog)', with 
'fintt-class honours, in 1S61, and iu the sumo year he was ordained 
Deacon by the Biiiho}) of Knche^^ter. He wiis first llceused to 
the curacy of Radwell, Herts, and in i86i was ordained priest. 
In 1863 he became curate r*f Poultou-le-Fylde. Thence he went 
to Melksliaiii, Wilts, and from 1865 to 1873 he occupied the 
positioQ of cui-ate-in-cbarge of North Meols, Lancashire. He also 
served on the committee of the Snnthport Intirmary. In 1863 
he married KVi'iA, youngest daughter of Samuel and Mary Mayhev, 
of Camberwell Park, Surrey. 

As incuQibent of St Thomas' Church, Lancaster, Mr Bone 
^^read himself in" on ttie last Sunday iu May 1S73, so that he 
bad held the living exactly thirty-three years. He was the oldeat 
beneficed clergyman in Lancaster in i>oint of length of time he 
had held the living. 

For some years he conducted a clat>8 in astronomy at the 
Storey Institute, and was never happier than when introducing 
others into the mysteries and deli^dits of sokr science. When- 
ever any astroufkinicsl phenomenon was observable in Lancaster 
his was the braiu tliat giudc-d local observers, !iti<l by hb 
personal observation of the heavens be has a' -s times 

been able to render g<HKl service to the cause niirnl 

research. In the work of the Lancaster Astronn itilic 

Association he took a deep interest, contribi nera 

on various phases of the planetary, solar, nta. 

There are many in Lancaster who entertain de 

to Mr Bone for the lead he ^avu thetu j >n 

aslronoiny. The establishment of the Gr^ k 

be was honorary Director, was mainly due i 

The sadden death of his wife in July 
to him, and for a time he was prostr&tei 



230 



Repm-t of the Council to the 



Lxm. 



and was able to resnine and discharge hia oiiuisterial duUn xap 
to withitt n few days of hia death, which occurred on Stukdav, 
27th May, at the age of seveiity-one. He leaves three aoostaJ 
two dau^btcrd. 

Mr Bone was elected a Fellow of the Society oa 6th April 
1887. 

A0NK8 Mary Clrrkb was bom, toth February 1843, M 
Skibberesn, a small country town in a remtite lurt of the Conntj 
Cork. HtT father was Jobii William Cterke; hi-r mother was 1 
eiatcr of the late Lord -Job ties Deasy. 

Very early in life she was attracted by the wonders of ifiP^ 
heavens, and before the age of tifteeu hod definitely formed tita 
intention of writing a history of ustrunomy, — hnd even actoallj 
hegiiri it. Alwttja doliento coiistitiitionidiy, she found her chiflf 
plea-iares in study and in mnsic. In 1S61 the family moved ta 
Ihiblin ; in 1863 to Queenstitwn ; and the years 1867-77 were 
spent in Itnly, chiefly at Florence, where Miss Gierke stndicd 
aaeiduouitly in the public library, and wrotu her first importut 
article, "Co|>ernicns in Itnly," which was accepted by the ^ib- 
burgh H^neto (October 1S77). 

The family tlien returned to England and settltrd in l^n 
In 1885 a])peared Miss Gierke's Hiaiory of Astronomj/ in the iVii 
te&ith Cetiturtf, a work now iu its fourth eiiition, and regarded u t! 
standard work, continuing the History of Grant. 

Miss Gierke's other works, published at intArvals, are ai 
follows ; — T}ifi Stjuiem 0/ the Stajt ; Familiar Studiea in Hi 
(in part only astrouoniical) ; The Herschets : A Concise ffietarj/ 
A$tr<»ioniy; VmNevu in A«trophijiic»\ Motfem Co»tnogoniea. 

Resides these works she contributed fifty-five article* to the 
Edinburgh Rmnew, mainly on subjects connected with Astnv 
physics : the articles on aatronomerd to the Otctitmarti of Nationai 
Biography ; some articles on astronomers and oa astronomieal 
aubjecis bu the Kncydopttdin Britamiica; und innuinexsble articles 
to Knowlfilgp, to Th' Obterraiory, an«i other periodicals. 

In later y«ar» Miss Gierke whr a freqnieiit attendant at th^ 
meetings of the Royal Astronomical Society, and in 1903 receirwl 
the great licujour of buing olcct«ii an HunMrar>' Member of th« 
Society. 

She was also a member of the British Astronomical Asaoeiatio&i 
and constantly attended its meetings. 

Miss Gierke was not a practical astronomer; but the thm 
months' visit paid by her in 1S88 to the Cape Observatory, as the 
guest of Sir David and lady Gill, enabled her to write wltt — 
increased clearness and confidence. In 1S93 she was awarded for 
her astronomical works the Actouian Prize of 100 guioeaa by the 
Royal Institution. 

Mifis Ctftrke'n ideals of life were lofty ; and, loving and lovabl 
her character was in complete harmony with them. In 
writings, Truth was ever her goal. 



^eK IQOJ. JSi^kiyacventk Annuai Chneral Meeting. 23 1 



I 



Accomplished in maujr directions, utronomy to the last vas 
ler chief iDtuLltictual laturest. 

She died, iifter a cotn|iaratively short illness — in perfect |io&ce^ 
ind fully conscious to almost her laat moment — on 30tb January 
[907. M. 1^ B. 

Thomas Rudolphus Dallmbyer was born in May 1859. He 
w the second stm of the late Mr J. II. Dallmeyer, photographic 
optician, his mother being the daughter of another famotu optician 
!— Andrew Koss. 

He was edacat«d at Mill Hill flj^bool and at King's College, 
London, and it had been intended that bf should go through the 
full university course ip mathematics and science. Unfortuuiitely, 
however, bis elder brother died suddenly in 1578, and his father's 
heallli aJM) becoiiiiiig impaired, it was considered deeimble that 
young Dalluioyer should relinquish his studies afttr passing the 
firat examination for RSc., in order to take a share in the manage- 
ment of the lirm foundei^l and made famous by ills fatliur. His 
father died in 1885, having batided over the busiuess to bis son 
the yt-ar before. 

He was thoroughly familiar with photographic optica in ail ita 
branches. Tevhaps bis hest work wiis that done in introducing 
and perfecting tlie leU-pbutogra^jhtc lens, and in working out its 
theory and applications in bis excellent book nn "Telephotography." 

In 1886 he l«scaiae a member of the Royal Photographic 
Bociety, and the interest which he took in the work of that 
society eventually led to bis election an President for the years 
1900, 1901, and 1902. 

Although he never contributed any pajters to the Society, he 
renderad many services to astronomy by way of supplying efficient 
tools. In addition to ordinary tolcscopes and pbotographic! U'Dses, 
of which many must have been used for serious astronomical work, 
he snpplied the six-inch Rapid Rectilinear lens viiik which the 
Capo Fhutugrapbic Durchmustemug was carrie^l out. 

He died on Christmas Day 1906, after an illnees of only a few 
days. 

He was elected a Fellow of the Royal Astronomical Society in 
May r888. - - ^, 



RoBEar laAAC Finnenorb was the son of 
lo the Atchblshop of CanLurburv. Wbea ^ 
eight years old the family emigrated lo Xal* 
the difated Minerva, which was wrecked oCT 
family being saved with great dilficulty. 
of bis parents that he should become a mil 
as a pupil at Ilisho[)Stowe under Bishop Co 
at Bisbopstowe being destroyed by (ire, } 
Maritsburg, where, in 1858, bo entered ib 
as pupil assistant in the Sorveyor-Genenl's 
year, while not yet Mventeen, he was p 



232 



Report of the CowkU to the 



hXVlL 4. 






clerk. Id 1864 bu rose to bt- chief clvrk huiI dreughuman, 
wsA alijo admitted u Ooverument land-surveyor. l)eing of 
ambitioiiH diBjKwitiuii, and tho Survpynr - General's departni 
offering no pro.-pert of furlher advancement, be succeeded id 
being traiufuri'L-d U> tbu Attoniey-Gcuerarn dc-iiartmeut, wbere 
he worked a* law^lerk luider Sir Michael Calwey for eleven 
yean. In 1376 he accopWd th« npijointment of PoeUnftiter- 
General During his tpnure ol office he intro<luced Bep«nte 
delivery winduu-n for Ktirr-peaiiR and nativeti, but his aU«mpi 
to ftitablitih a poi^Ud delivery was unsuceesaful. In 1S77 be wii 
appointed Miister of tlie Supri*me Court, which post he held 
March 1881. He was Cliairman of the Zulu War Commis*! 
appnint«d to decide upon the rompeuAation !« be paid to relali 
of those who bad fallen during the war; «nd for bis '^adniira 
report," drafted with the assistance uf Sir Henr>' Bale aud D 
Green, he received the thanks of the Government and an expreat 
of the (iovernor's high appreciation. In 1894 a new office 
Cniwn Solicitor and ParlianK-'ntary BruugliL^mau was created^ utJ 
the then Prime Minister, Sir John Robinson. ofTereU thu post to 
Mr Finuemore. It waa in thin capacity that he, in 189 
acwmpinicd Sir Widter llely-lltitchioson to Vulksrust ns I 
adviser in connection with the Jameson Kaid. In Noveni 
1896 he succeeded to the Supreme Court Bench, and during 
of S903 and 1904 he acted as ChiofiJuattce, and towarda Uic 
of tbo latter year be retired. 

Apart from these services as a public official, Mr FinDem 
did nmcb to advance the cauaa of philanthropic, religious, 
social ■•r^nisstioud. He was an entbueiaatic FrueiuuHon, and b 
the oflRw of District Grand Muster from 1882. To the cause 
lemperanre be devoted much titue ; and ha a member uf t 
Wesloyan Methodist Church he did much for the atlvuDcem 
of that body in Natal. Me was, beiddes, a Fellow of «aob 
the following Societies : — Royal M»tt<«troli'pical, Royal >1 isior. 
Zoological, Kuvh] Geugrapbical, Statistical, Anthropological I 
tioi), Royal Coloriiril In»>tituCc, and the Imperial lustitnte. 

Mr t'innemore died 27th July 1906. 

He waa elected a. Fellow of the Society in November 1 8 

J08EFH H. Frbbhan waa bom, 18th April 1845, at Stratfc 
Essex, where he re.sided all his life. A Achoolmsiiter by [irofe&Mr 
be devoted much time to pupular lectures on astronomy. }] 
preference for astronomy was due to his grand ftit her, Mr Jnli 
Freeman, who was an intimate friend of Mr Epps, the 
Assistant .Secretary of the Royal Astronomical Society. 
Freemau was for many yeara a nioiit regular attendant at 
Society's meetings. He died on 51b Februarj- igo6. Ha 
elected a Fellow of the Society on the lotb Noviimbor 1871. 

JcN9BPn Gledhill was bom, lytb November 1837, at Bradfc 
Yorks. His early training was directed to tb« profession of 




I 



EitfMy-uvejUh Annual Oeneral Muting. 233 



•Rhocihnaftter, wliicb he followed for eome years. Hie own tastes, 
however, gradually n-nn him over to the close prosecution of 
scientiHc Btudy, and in 186S, wheu Mr Edward Crossley csUbltBhed 
b)8 observatory in Halifax, he asked Mi- GledliiU t*» undeitAke 
the work nf observer. The meaAUTvment of double starti was 
a distinj^ighing feature of his work there, and the results were 
ernbodietl in A H'ljuUiook of Dtnthle Starn, which wan wriltno 
witli the co-operation of the Rev. J. Wilson, M.A. (now Cauou 
of Worcester) and Mr Crosslej. He alao contributed Mveral 
papers on planetary obeervatioDa to the Montldy Notieet 0/ 
the R.A.S. 

The erection of the 3-foot reflector in 18S5 {built by Dr 
Couimoo, aud subsequently preBouttid to the Lick Obeervatory 
by Mr Crosslay) promised a more extended sphere of work, but 
it van found that, for purposes of exact obmirvution, the climate 
of Halifax was hopelessly ausuitable, aud the serious use of the 
telescope was soon discontinued. 

After abiiut two years of Indifferent health, Mr Gledhill (wKin 
after Mr Crossley's death in 1905) removed t»i Ilotldesdon, Herts, 
where he died on 20th March 1906. 

His scientific attainments were by no tneaiui a complete in- 
dication uf hitt mental activity and varied taatos. Ho was ail 
omnivorous reailer, a very fair amateur violinist and organist, aad, 
later in life, became an enthusiastic fishenoaii. Apart from his 
more serious work in astronomy, there are probably not a few 
amateurs liviu;; who Imve at some time or other felt their iudehted- 
ness to hu ready and willing asaisPince in their littl<^ dilHcuIties. 

Mr Uledhill was electi^d a Kellow of the Society in Ma}' 1S74. 



F. U. O. 



7. 



I 



"William JoHNSTfi.v was born, jothAuguyt iSig.at" Stockholm 
Farm," in the parinh of Dunifriee, Scotlmid. He was for many 
years a furniture nmimfacturt^r in Gloiicester, hut later dealt in 
curios, becoming an authority both in Kngtatid and America, In 
1843 he married Miss Avery, of Gloucester, who died in i8g8. 
Ho was interested iu a variety of suhjccUo, as may bo judged front 
the titles of his jAmphlets, — TVie AtwMnerg of thu Htavent; The 
Immortality of all Liring Greaiureji; Ars Inio^i'-atinff Beverag*:> 
Neceg$arie$ of Life t He died on loth January 1907, leavir< 
ions and four daughters. 

Mr Johnston was elected a Fellow of the Soci« 
January 1897. 



Alprei) Euwabd NiCHOLUt was b»ru in 
'Gloucestershire. Immediately on leaving scho 
and after serving in all grailes as a mariner, id 
a small nautical school in Limeh')u»e, of wh 
in 1894. Under his management it becac 
cessful schools of navigation in the countr 
the Passmore Edwards Sailors' Palaco at L 



234 



JUport of the CouiuU to the 



LXTa4. 




the .school was transferred to that building, where it hug siooe b( 
carried on under tho name of the King Rdward VII, Nautk 
Hcliiml, and hag had many amoii(; its Htudents who have 
ht^h in the profession. Caiit^ain Xicholls nas the author of mvg 
works on navigntion and astronuniy, including Senmattxhip at 
Gui/ie, and Goncuie Rule* to lioarfl of Trade F,raininaiio7i«, 
was a member of tlio Britiflh AstrumnnicaJ Association, and hi 
taken up work in connection with tlie Variable Star 4Sectioii. 

He died Buddenl^', from the result of an o]>eration, on 4th Marfl^| 
1906, l(>aTing a widow aod six young children. ^H 

He was elected a Fellow of the Royal Aetronoinical Societ; 
in March 1905. 

RoaBBT Rawson was born at Brinnley, a small colliery village 
nine miles from NottiDgham, on the ssnd July 1S14. Uiit father, 
John liawsnn, wan a man of THty limited tneanK, whoFtft life seeoii lo 
have been a long struggle against adverae circumstances. 

Robert Ruw^un wwi a child of eeveu when he bcxan work in the 
coal-mines of Messrs Rirter & Walker at Kastwood, two or three 
milfB from liii^ Imme at Brindley, and he never forgot the long 
walfeg in all waath<>r8 to and from the mmeB. Tt waa tluring 
this sixteen yean^, when working a.s a collier, that he laid the 
foundation of his future buceuss. One day he came acrosa a 
periodical cotilaiuin;; a variety of Tnathematicat quBAtioQS, to some 
of which he could n^e. the amtwer ; hut not being able to timeier al 
be made inquiries and was told that he wanted an " arithmetic.' 
Accordingly, one Saturday afloriLoon, on leaving tlie i>it, he walk 
iato Nottingharti and bought a second-hand artlhmetic for t 
pence, 'rhi^i hr^ utted to find the answers to the particular queBliooJ 
he never worked through it. In the same way he acquired 
algebra, then an old Euclid, and more advanced worka. lo 
1837, when Robert Stevenson commenced building the I^faitohester 
and Leeds Railway, Kavvaon obtained employment as clerk aod 
dranghtsniiin in a couHtructor's nthce at Rochdale. Ho did cot 
seek thiEi situation ; it wan offered under the following circa oiKtaiicea. 
A contruveray arose in a local pajier as Lo how the level of the 
road should be altered at a curve in the railway, bo aa to 
counteract thi^ effect of centrifugal force. Rawson ^ve 
ftolution, and a few days later the railway engineer sent for him, 
he presented himself in collter'a dress and sjioke the L-olli 
dialect, there was at first some misunderstanding. In the end 
was urranged tluLt ho Hhould luuve the mince and i^o to the offi< 
When the railway was completed in 1842 he removed to Manches 
and beimme a teaclier nf mathematics, and kept up a correspondence 
with the York Courant, the Matk^matinoji, the Ixuty't <md 
Gentlemaii't Diary. He aUi> wroic papers on the " Bammatioa of 
Series," " Definite Imegration," etc. etc, which were published in 
the Mfiituiirs of the Manchf^t^ter Literary and I'bitosophical Society. 

In 1845 he joined the Manchester Society, and two years lalsr 
had a seat on its council, where he came into contact with leading 




Feb. 1907. Eighty-Hwnth Annual General Muting. 235 

practical engineers aod chemists. At this time he was employed 
by StevKu-Mn] to calculate the Htreas on tbe girJcrs of the Meoai 
IJrid^e, and by Eaton Hod^kiusou to determine the strength of 
cast-iron pillara and uther iimt<?riiils. 

In 1843 the Admiralty eatabliahed a school in each of the 
dockyard!) (or tbe education u\ engineers and shipwright ap- 
prentices. The instruction vraa at tirst given by the dockyard 
tilEotirs, but in 1S47 tt was cuusidered that properly t|ualified 
masters shotild be appointed. Hodgkinson, to whom tbe First 
Lord applied, recommendeil Raw»oi), who was rather dubinnn, as he 
had never had experience of flrhoot life, in fact had ue%'er set his 
foot inside a school. However, for a period of twi'Dty-eipbt- years he 
held the po6t at Portsmouth with credit to himself and advuntage. to 
ht» piipiU. Many of those passing through htA ^bonl are now Blling 
places of high diKtinction in the service of the vVduiiralty and lA 
th*; gi-eat shipbuilding yanls. It will suffice to mention Sir Philip 
Watts, K.C.B., the prest-iit Dircct-<ir of Naval CoiiBtmction ; Sir 
John Diirston, K.C.B., Engineer- in- chief K.N. ; Sir JamBs Wiliiam- 
MD ; and Hrofessor Francis Klgar, F. itS. 

While at the dockyard school he was appointed by tbe Lords 
Comniissiouertt of the AduiiraUv to make ex^K-riments, in con- 
junction with the miister sliipwright, John Fincham, to test the 
validity of Moseley'fi forniuhv for the dynamical stability of sbips. 
Muaeley gives an account of thexe experiments in a paper entitled 
"On the r>yniimical Sttibility of Ships and on the Oscillations of 
Floating Botlies," in the PkHomphical Trantacttom, 1851, and 
speaks in hi;:h terniR of Itawson*^ ability. 

Kawann devised the screw compafa, which doterminee at sight 
the pitch •->{ tbe screw : for this invention he received the thanks 
of tbe Aduiimlty. In 1851 he published a treatise on Hie 
ScTtic-ProptUer : an Inceatigaiion <>/ its Geometrical Fropertiu, 
and some elementary works un arlchmethic, mensoraLioa, and 
trigonometry. 

The great bulk of Rawson's papers are in the Memoir* of the 
Maiichester Literary and Philosophical Society, but some will I»e 
found in the Hritiph Assooiation Jteporfa, the NavaJ Anbileria' 
TrantartioTtM, and the Meaaenger nf AttU/tetjiaiiet. Tbi 
deal with diOerential equations ; prime nnnibeni ; fric 
us<-'iUation of floating bodies; Htability nf shifts ; k> 
et<;. etc, hi** Uisl paptrr Winy on " Dr Ferrure' Tha 
Nuraberc" ia the Mf^ntenger 0/ Malhematir/, 1805 

In April 1894 be was plareil on tbe roiinuv- 
for tbe county rif Uanipahire, and, nulwithhiiiiUi 
he diitchnrged his duties an a magiatnlc with trr^i 
up to within a month of bis death. He wiia twic 
1851, tu iMrs Balduck, daughter of his friend . 
again, in 1870, u> Miiw Aylword, lUughtcr 
shipwright in Plymouth I >o(kvurd Tlirre 
either marriage. Mr Raweou was a man a 
temperate living, rising at 5 in the mnniing 



236 



Beport of the Council to the 



LZTIL4, 



QKO 



in tlie evening. Hin days were tiiieut workinic in bis |{ftid«i, 
walking and cycling. Tu the spring of 1906, wliilc out walking st 
6 o'clock on a froety morning, ho slip]>ed and briiined 
An attack of intiuenKa supt^rveDed, which develojied into pn 
and on nth March he die^l at the advanced af:e of ninety 
Mr RavoDii wits 0110 of tliuse men whu inspire aflt-cLiun antl com 
the homage of heart as well &s intellect. At his fiiiiera), whic£ 
touk plac« i6th March 1906 at the Uavaiit cemetery, were, bwi< 
the repfesentJitives of the leading county families and a niinilter 
his fellow- magiHtratea, many of bin old papilK, Homp of whom 
travelled K^at distances to pay their last tribute at respect. 

Mr Rawsun waa an As»ociaLe of the Lialitute of ^aral 
Archit^!Ct«, and a memlwr of the Loudon MiitheniaticiiJ Swietj. 
}fe wa« elected a Fellow of the Itoy^l ABtronomical Society on the 
9th Kovemher 1889. 

\Viu.uH John Ktetnolds was the eldest son of WiUtam 
Keynolds, a carmine manufacturer of Hackney. He was bom al 
L'lapton 2nd Septembff 1845, and attended the local achoola, and 
uflerwardtt a boanlinf<-;nc)ioo) at Greenwich, and finalljr Homertoa 
College, at that time audor Dr Uiiwiu. Being of a mechanical 
turn of mind, hu was bound apprentice to a lirm of piauofort* 
makers in Clerkenwetl. Thia firm coming to an abrupt end, 
RejnoldH became clerk in ttie oilice of the Metro[)o]itaa Drinkiok' 
Fountain AsHOciatioti in Clemeut'sr Laue. At his father'^ df^atii, 
he, in conjunction with his brother, carried on the njannfactttreof 
carmine «t Hackney for many years. Finally he joined with Mr 
Fred Baddeley, forming the firm of Baddeley & Reynolds, engra^-en 
and die-aiiikers, in tlie Old Bailey. 

Mr ileynolde married in 18S0 and had one daughter, fie 
seems tu Lave interet^ted htni»etf iti many subjects, and esj>ei:ialiy in 
Horology and Astronomy, and often answered the que^tion^ ot 
inquirers in the English Mechamc. He also intere«t«J him^eir is 
social mattera, bein;{ at one time Secretary to the Aouth Plan 
Ethical Society, and wiis a man much eHtecmed amoug«t bit 
acquaintonoea. Hik death occurred on 15th July 1906,81 "Vamo," 
Palmer'* Oreen. 

He was elected a Fellow of the Society on i ith June 1898. 

Philip Edward Sbwrll was bom in London on the 141 
January 1822. Hia father, Isaac Sewel], wa* a member of 
Siiciety of Friends, and bis mother {uM Mary WnVht) was a Ia«l 
of some literary repute. His education comuieuct^d at Hacku< 
Grammar School, thoo in charge of Cuudu Eden, and finishc^l al 
the Frieml.s' School at Stuke Xt^winjiton. On leaving school 
joined the London and County Bank at lirighwn, of which 
father was manager. Shortly afterwards he waa entered fd 
Cambridge Uaiversity, but a breakdown in hia health nueesaitatii 
an outdoor life, he took up civil-ongineering, under Mr C. 
Vignoles. In 1 849 he married Sarah, youngest daughter 



Feb. 1907. Uightif-seventh Annual Geneml Meeting. 237 






I 



Samuel Woods, of Tottenlmm. He wu5 engugtM) in the con- 
struction of the Settle and Carlisle Kailway, and Bub»;(|uently 
in engineering work upon Seaham harhonr. In 1853 lie wAnt 
to Spain as niilvay engineer, and while tlier« be entertained the 
members uf the Himalaya Ec1ip.se Expedition in June i860 al 
Santauder, for which hi- received the thanks of the StKiiety. In 
1864 he accepted an appointment in GurncyV Utmh : aod when 
this bank, in 1896, as8uuie<l the dtyle of Barclay tV Co., Mr Sewell 
waA elected one of the Directors for ibn JS'orn-ich District. 

Mr SewflU was a man of broad iiynipathieM. In the |)ariah of 
Buxton, where he bad properly, he was greatly interested in the 
Hefurmatory for juvenile offenders, which be pmctically kept ali»e, 
Itotb morally and Knancially. He was aUo an active worker on 
behalf uf the Discharged Prieonent' Aid Society, 

Mr Sewoll was a justice of the peace, and was one of the 
original Aldenuen appuintcd un ibe forroaliou of the Norfolk 
County Council. Mr Sewi-ll wiui twice married, but he died a 
widower, leaving one son, Mr I'hilip Edwnnl f^ewell. 

Mr Sewell was elected a Fellow nth .Taimary tS6i, and died 
6tU February 1906. 

William Sihmm. who died on 2nd -tanuary last at the age of 
eighty-nine, wa» the oldest Fellow of the Society, having been 
elected in 1851, three ye.ars Iwfore any existing Follow. The 
natoes of Tmn^htun and of Siroma have been sd lon^' hoDOurably 
aaftociatad with the history of practical aHtMuomy that the oppor- 
tunity may be tiken to recall a few facts about the difTorent 
individualH vrho have borne them. 

Edward Tntughton (t7;3-i835) was admitted as a young man 
to partnership with bi.-* uncle uf the sane name aud hia eldest 
brother John, who were m>ttted in London as mathematical instni- 
nient makera. About 1 783 the Trongbtons established tbeiuselves 
in Fleet Sir»;et, where thcv w.»u»menced an independent busincjia, 
called " Ve Orrerv," a^ Aucceiuuirn to a series uf well-known artints 
(Wright, and subsequently Cole) who had previously ocmpied the 
same premises. After the death of bis uncle and bib brother 
Jolio, Edward Tr^iughtoD alone continued the buAinoss until 1826, 
when he U*6k Mr William Simms {1793-1860) as his partner and 
succesBor, After Troogbton's retirement in 1831^ William Simms 
cuntinned the business alone till hi« death iti ? rf 'i; 'r was 

BUCveeded by hJK sun Jsmen Siiums, the present 

William Simms had liv<i brotbors ; op> 
Walter Simms ( 1803-1865), wo.s for a shoe' 
aasi-ilant at the Koyal 1 'Wrvatory undei 
of our Society ; ond another brDth<^r, .lo' 
of Hhip.-*' and other conii-nsse* in ' 
Our receully deceaaed Fi'lbm, Wil 
son of this brother Jantvs, and vmi> 
father's huninew. lint aboiit 18:'' 
had commence! 



23& 



B^H of the Council to tM 







and surveying: instruments) seemed so much more promUing 
that of A corapaiw-iiiaker, that he was led to apply to the woll 
kaown firm tor a eituation, which waa easily found for him. 
l>cc&me sit peri til end e lit of thit busine^f!, »iid aflerwarde a pi 
with bis cousin; but in 1S71 (after beiu}; partner for some 
years) he mtirad, during a loss of hc^alth which he regarded 
piTinanent, but which fortunately proved only temporary. 

The Monthhj Xofic/vi contain several papers by " WUUam Siin 
jun.,"* especially on thi^ impruvemeiit of infltnimeiita. The 
in the central cube of the Greenwich tranttit-^ircle telescope 
first suggested by him, uccordio^' to the retToUecticn of Mr James 
himma ; and (on the same authority) ho greatly irapro%-ed the 
cutting apparatus of the dividing macliinett, while aa a band- 
dividtr he could scarcely be excelled. For a long time he «ru 
employed upun the cunstnictiun uf the National Stmidard of 
length, and greatly nsflisted the Rev. K. ShE-cjishanks in that w«rl 
a large number of the ob^ervationA, an welt a^ much in the way 
construction, being due to him. He alao helped the elder £01 
Rosse, ]mt up Mr Carrinnt-in's telescope, and did work al Bids 
Observatory. Hia astronomical inlerests were wide in ruiige 
his daughter (Mrii M'Liiclilan) well remembers an occasinu wh 
letters announcing some interoatiug and novel observatinn mad 
indepvudeutly by Sir George Airy and bimeelf crowed in tiie post* 
We learn froiu her aluo that ubiicrvatiuns on the Sun caused the 
loss of ht-r father's eyesight. 

Whik- in husinesi*, and uftwr hia marriafje in 1844 to Chariot! 
daughter of Francis Needham, of Wymondham, Leicesteriihi 
William Simuis lived at Granville Square (in Luudun), at Patna; 
and at Cliarlti-iQ. After his retirement he lived at Burnhani, 
Somerset; and iifternards in the UIk of Wight, at Uytle am 
Shaiiklin. He had one mm, who is u ttnrvcyor in New Zealan< 
and ihe daughter above mentioned. His widow wurvives hi 
aged ninety-six, and aUo quite hiiud. The late Queen waa madi 
iuterei^ted in the aged couple, and abortlv before her death Mr 
Williatii SimniH wm gnmte<l a small Civil List penaioD, on acconoi 
of his blindness, caused by devotion to science. 

TTe \rtuf> horn in London, 22iid June 1S17; and died at Albe. 
Lodge, Shautdin, LW., 2nd January 1907- He was elected 
Fellow on loth January 185 1 (the Report of Jurors of the g 
Exhibition of 1851 mentiona his management of the Astronomical 
Kihibitu), and served on the Council 1867-69. a. h. t. 



berlfl 
lieal^ 

I 



The Rbv. GicoRaB Vbkablss was Wo at Hainptongay, Oxo 
24th A[iril 1S21. He was educated at St Kdmund Mall, Oifd 
where he took the degree of Student of Civil Law. In 1843 
marric'i Mii^ |)avi« of Loudwater, Iterku, by whom he had atx 
children. The wife and one daughter uurvive him. In 1852 ha 

' In one case tlitre k Hom« cotifnaioa with another "WlJIiini Simii 
tuor.," Kttt'rwar<tfi de»mbeil is W, H. SIiiiiiih. He was the am oT WtllUi 
Simnis itin eUi-r, and brotliir af thn present wk- raprcsuiitativo of the firm. 



Feb. 1907. £iff/U^'Sevefiih Anmtal General Meeting. 239 

W8g ordained priist by the Biiibop nf Oxford, and fiuall j appointed as 
fint Vicar nf St Paul'«, Cbalhaui, 1S55. lu 1858 bt accepted tbe 

[private living of Friezland, in tbe West Hiding of Yorkshire, which 
he left in 1 870 U> become Vicar of St Matthew's, J^icMter. Tn i S74 
be was Lraneferred to the important vicarage of Oreiit Yarmouth, 
and in 1881 be \vu« made u Canon of Norwich Catbedrul. Finally, 
on the uominatioii of the Lord CbaQcellor, he liecame Hector of 
Burxb Cajitle, neur Great Vaniioulb. White at Great Yarmouth 

[he did lunvb lo restore the historic pariah church, to which be pre- 
eeot^l a msgniticent oak pulpit. Canon Venahlea wa^ a prolific 

, writer on Church mattera. He was a member of \he Royal 
Commission ou Patronage, and wtis select Preacher at Cambridge 
iu 1883. His death took place jotb Deeonibor 1906, at the age 
of eighty-five, lie wjw electBtl a Fellow of the Society on the 
nth of J:iniiary 1856. 

Sauubl PiSRroNT La?iolst was born at Roxbory, Maasa- 
chitftetto, on 2and August 1834. After he harl grndnated at 
Ilogton High School in 1851, he took up civil-engineering and 
architecture tui his profe.-uion. From childhood he had shown 
groat devulion to scicnittic pursuits, especially i'f astronouiy. 
H*s practii^ed bis prof fsa ion fur simie thirteen years, Imii after 
spending part of Ibe yeara 1864 and 1865 in travelling m Europe, 
and visiting foreign olwervatorifii and leanieil institutions, he 
decided on bis return to devote his life to the puMuit of science. 

His Brst scientific a[)pointment was that of Assistant ttt the 
Harvard College Olwervatory in 1865. In the fidlowinj; year be 
wa^ made Assistant Professor of Mathematics in tlie NaVAl 
Academy at Annaitolis, a \>ovX ho almost immediately relinquished 
to become I'irvctor of the Allegheny Observatory at Pittsburg, 
where he reiniiiiied fur twenty years. 

In 1867-68 he was busy witii tbe equipment nf the obwjrvatory, 
and a litlle hitter I)p arrnngfd anit dLrrte'l out a ]dnn fnr distribut* 
ing standard observatory time to the exUting railway sytttem of 
the country. In 1S69 hu wunt U* Kentucky, in charge of a pirty 
of the United States Const Survey, to olM«orve the total eclipse of 
the Sun, and in 1870 he joined a Qovemment eclipse exi 
and went to Jerez in Spain. The only obher Dcl)|Me oxpt 
took part in was une to (vbserve the e«Upae of 187S fr 
of Pike's I'eak. 

Htm firdt interest at AlieghsDy was the 8ud, on 
he was there that be made his well-known drmwi 
and other details of the Suti'» surface. An iimii> 
said of these drawings that the better tbo d 
surface is 8een, the more closely do«8 it f 
drawiogs. 

It was about 1875 thtit be began to devo 
the meaAoremcnt of the b<wt spoctra i>f tbe 
tMMlies. Experience coaviuced hJiu of the 
thenuuptle as a roeuuriDg iustrument, an< 



240 



Report of the Council to the 



LXnt 



I 



yv&n lit was succeasfol in the invention of the Bolometer. Tb: 
iustruDieul) a.s is well known, ia ati electniAl thermometer on 
priaci[)Lo of WheuUtuiiu'a bridge. With it bo at once set to wi 
to explore the infra-red spectrum of the Sun : he Bxt«aiied it Ut_ 
regions of ten times tbe wave-length of the visible spectram 
mapped the lities in it ; other reaearohes mtb the bolocneter wen 
the actiou of the Ehi-Ui'k titmuupherc iu Hailt«ring and a 
Selectively the Suh'b raya of all wuve-lengtbii ; on the m 
spectntiii i>f the Moon, and & iletertninaLion of its Lem 
which he found to be a littk abi>vo o* C. ; an estimate of 
conxtaiit of w>)ar riulititton by a nt>w method ; and on the oonnee> 
tion between teiii[)craturc and dtstnbuuou of radiation in tbe 
Bpectrum of heated terrestrial sonroea. All this was done bet 
f 880 And 1S88. 

In 1888 lie was appointed Secretary of the Smi'thsoniu 
luatituttan. The Smithaoiiian Institution officially represent* the 
interest of the United Stali-^ iti science, and the chairman of iti 
boari of directors is the Preeldent of the United Stat^^a. lb 
immediate affairs are administered by the ^cretary, who hu 
charge of many and various scientific interests, 9uch att rhu National 
Miuetim, the Intarnatiuiial Exchati;^'e», the Bureau of Auicriottn 
Ethnoloj^y, thu National Zoulngiod Park, and others. Theas 
S'lminiDtraUve iluties neresHarily ciccupied much of Langluy'i tinu^ 
and it was niiw impoesible for him to devote the same pe: 
attention to hia scientific i-eaearehea ai< before. 

A few yeAHf after hirt appoiutment be founded the SmitbannitA 
A-ttro|>hy)iica] ObM;rvatory, the object uf which was to increaao our 
kniiwiedge of the natural a|i;encies which control climate and h'fc 
One of the mfwit important of these he believed to be the amount yf ' 
beat radiatml to the Kartfa by the Sun, and at tbe lime of liia df«tit— 
he waa engaged in the prohleiu of finding whetht>r the amount W4« 
constant, or varied aafficiently to affect the climate of the Earih. 
About tiio same time he improved his bolometer by adding to it a 
]>li olographic arnuigument to rei'ord its readings autamatically 
and continuously : by its meari» it hpcrame pojtsible to map the whole 
uf the energy spectrum of the Sun in a few minutes. 

Perhaps Lnu^ley was mort^ widely known for hia studies in tba 
problem of flight than for Ina astrophysical work, or hia abb m 
dire<!tinn of & great institntinn. lie bud alwaya bi^en int«rested infl 
the queation of flight, ami lirat took it up seriously in 1S89, lo 
1891 he published Itis "Kxperiments iu Aer>idyuaroir8,"and in 1893 
"Tbu Ititerual Work of the Wind," In these jtaperB be demon*. 
atnUvd tlif theoreticiil pn^sibility of fli;<lit by means of larfctj 
auntainin}^ surfaces and nieehnnicnl motors, and for the remaiiUDgJ 
years of liia life he gave much time and thought to iU" practicalj 
realisiLti'iD. f/irge niud<.-lii of Ids desi^^n for a flying machine 
8Uccessfully flown between 1B96 and 1903, and he was encouraged' 
by hia auceeaa t.'> construct an aerodrome Iargf> enour^h to carry a 
man. Two triala ot this machine were made on th*- Potomac river 
in 1905, but were failed by accideuta iu the launching, furtunacety 



Tab. 1907. E^hiy-Kvtnlh Annual General Meeting. 24 1 

• without !oM of life. No further trials were made owing to a com- 
bioition of unfavourable circumulttiiccii, iucluding fniling health. 

Liiugley's (lubliahed papers are over a hundrml in number. It 
[tvaH his nim in all bis publicationH to writi^ them in the simplwt 
and cleari'St language, so that they might be uudt-rstood by 
educated |wrsons nut specialty ruad iti the loibject, and he took 
immense paiuH lo try tu nchieve his aim. He wan u Foreign 
Bfember of the Koyal Society of Loudon, a Curre^pondent of the 
IiiatituUi of Friince, Member of the Awwlemia doi I*incei of Rome, 
and of many others. He received the degree of D.C.L. from 
Oxford, and ScI). from Cambridge, buidee muiy otlier honorary 
degrees ; nud he was a medallist of the Koyal Society uf London, 
thy American National Acaduitiy of Sciences, and the Institute of 
FruDcc, and received tlio Diplomo of the Koynl Infttitntion. 

Ue h»d many interexiM outAide bis scientific- work. One was 
psychicjil research, and for uiatiy years he was asLsoriated with biith 
the Aaieriicau and the liritish Sociuties for Psychical Ue.'iearch. 
Kl' sliowod a keen appreciation of the best tn English and French 
lit*^rature, and had a special interest in George Horrow, of whose 
mannficriptfthc bad a large colloctitm. He wiis also much iuterested 
in the line artA, and had a cunsiderablti knowledge of pictures. 

He died on tha 27tb February 1906, at Aiken, South l^arotina. 

Ho was fleeted -A.isociftte of the Royal Astronomical Society in 
1883. a. c. 



/. 



JsAK Abraham Chr^.tirn Oudbuanb was born at Amaterdam 
on the 16th of December 1837. At the age of sixteen he went to 
the University of Leiden to Ktudy uHlronouiy uuder Professor 
Kaiser, and took his degree in 1852. In 1853 Iir was apfiointed 
a« Astronomer at the Obttervatory which wus then established on 
the rnof of the University building, and occupied himself ma-^Uy 
with observation A and compntations of planetn, cotnetx and variable 
stars, which are published chiefly iu iho A^troTiomische If achrichf en. 
His first astrououiical publication, however, dates frt^ni 1846. 

In 1856 OudemaiiB vra» named Professor of Astronomy at the 
Unirernity of Utrecht, hnt the following year he Teaigned hta 
professorship to take up his appointment of Chief of the 
Geographical Service in the East Indian Colonies. Th<'r '^r- 
determined, in different parts nf the iirchi{)clago, the If> 
longitude of a ^^reat number of tttation!!, and executed 
of engineers the iriangulation i>f the whole isbmd c \ 

found time for more strictly aaln^uoinical work, • 1 

total solar eclipses, and takiug part in ih^ 
transit of V'enUM in 1874 as Chief uf tin* ' 
inland of Reunion, hi« colleagues being 
Professor Kaiwr. 

In 1875 he returned u» Europe, an 
time, HrofesBor of Astronomy and I.>ire< 
Utrecht. Thin position he held till i8( 
age of seventy years. 



242 



Report of Uie Council to the 



LXVIl. 



Wben in Batavia he published the first part of the nipasui 
of tlie Wc line n«;ar Sunplak in Java, the secoDt) part 
pubh'ehed shortly after Lis ruturu tu Holloiid. When all 
ob^rvationfi for tho tiiimgiilatiun of Java wore completed, he vu 
charged bjr the ([overnraent with their reduction. Daring the 
years tSgi-1900 he piiblt^Led the results in four lai^e volumoe. 

As a Dieniber nf the T.iutch (reodtitic Committee, Oudeinau 
had the direction of the geudetic aatrunotaical obserTationa, and is 
1905 he pub]iiiht;d a voluruv containing the results of tbe observo- 
tionn of latitTid<!i and azimuth mode at ihirteeD stations, togetln 
with a studj of the inntrumentri employed and nf their diflTeiDt 
errors. Kotwjthataiiding his Dccu(>ation with hie geodetic woi 
Oudcmans pabli»bvd a ^rcat iuirnb(>r of papers on differei 
atftrnnomical nuhject^a, e.g. "(Jn the theory of inBtrumcnts' 
the ring-ftydtciii of Satiini " ; " On the poaltton of the equator 
Mars"; "On the Moon's diameter"; "On the parilUx of tixeJ' 
stetv." 

lie pnblishifd also a popular work on astiunomy for tbe schools 
in JavH, iind revised Kaiser's Popwlar Astronomy, llie Starry 
Heavem. 

<)ud<'iuan» was indefutigably buHy with aHtronomical work tn 
the end of hi)i life : ordy somu few duyii before his death ha 
i:orrecc*Ml thi^ proofs uf his lant {>apur, "On the mutnal occultatiotii^^ 
and actlpiies of tbi> Satellites of Jupiter," published by the Acadeiii|^| 
nf SctencuH at Amsterdam. He was a painslakitig ostronomer,^^ 
with a vast km>vi-le«lKt-, who tci all hit* work utruvo his utmoat to 
attain the highest nucuracy and completeness, lie had u noble and 
opon character, and was much esteemed and beloved by all wh" 
knew him. 

His deulli at the age of nevcnty-utne took place, after a shoal 
illness, on 14th Detioniber 1906. 

He waiii t;lected an AiKiOciate of tbe Royal Aatronomicfel 
Society in 1&S3, and a Corruspondent of tbe French Academy in 
1901. H. <l. VAN o. 8. K. 




feb. 1907. Eighty-seventh Anntutl Generai Meetiiuf. 243 



PROOEEDINQS OP OBSEBVATOIttEft. 



Royal Obfervaiory, Oreentcich. 
{IHredor, Sir William Ckrixtie^ K.C.H., Asirotumier Royal.) 

Traiu/it Circle. — During tho year 5877 observations of tranxits 
[■Had 5605 of meridian zenith distances have Ijooii obtaiut-d. The 
IStui haa been oliserved 125 times and the Moon 94 times. The 
[lunar crater Mbstiog A has also been obstifved 47 times. Reflexion 
I obsen'atioas of atani have ))ceu obUiined on 69 nights. 

The objoct-glass of the transit-circle was repolisbed at the 
bej^ioning of the year, hut in the proce-w the figure was affected 
owing to the thiauesa of the leiiaes, and it wan not til) tlie end of 
April that the refiguriiig was satisfactorily completed. There waa 
oonae()uently much ititermtitiou in the ubsvrvatiuno during the fintt 
four months of the year. 

Borne obnervatloDB -with the reversion prinni, doeigncd to 
H ascertain whether the directiuu of motion had a systematic effect, 
m revealed the fact that the adopted wiru iutervuls were sensibly in 
error. It had been assumed that when one or two wires were 
renewed the intervals of the remainder were unaffected, but it 
now appearft probable that the process of ioMrting new wires is 
liable to displace the existing wiren. A redetermination of the 
intervaht of the wires for the periods covered by the forthcoming 
Second Nine Year Catalogue, 1897- 1905, was undertaken, 1200 
iranaita bein^' worked up in each year. The result of thi« extensive 

» discussion discloBod eensible errors in the adopted wire intervals, 
but OS these are of the nature of accidenuU errorw, no corrections 
have been applied to the transits, the Bystomatic effect on the 
catalogue places being presumably negligible. 

The reductions for the .Second Nine Year Catalogue for 1900 
are progressing. The r.fines from the I'ole to 15' N.RD., Part ii. 
containuig the astrograpbic reference ataift, are completed, and the 
copy for presa ready. Some tzoo of thwe stars which are common 
to the Carriugton Catalogue for 1855 have been com^iacod with it, 
and from the comparinon,, fitter corrections for Bystematic discord- 
ances have beeu applied, proper motions have been Heterminod. 
K These propur uiutiuiiK an<t those derived from the new reduction of 
f Groombridge's Catalogue have been used by Mr Eddington as the 
data for a paper on the ".Systematic Motions of the Stars," in 
which Kapteyn's two-star drift hypothesis bae been examined * ' 
iDdependently confirmed {M. N., Ixvii. p. 34}. 

The new working catalogue, us stated last year, conv* 
reference stars down to g^'o in the Oxford Astrographic 

I between the limits of 34* and 32* north declination. 1 
fundamental slatB will also be observed. 




244 



Report of the Council to thi 




i 




AUazimuth. — This inittniinent has been used as a m 
tnuuit instrument during the second and third qnarLt-rs of 
M[>ou for the nb^ervation of the Sun, Moon, plaaeie, And 
st^rs in Nevvctmli'd Fiiitdaiuental Cataloj^e- Thb inetrumeDt 
reverseil evi>Ty two months, alternately by reversing in its T«, ti 
by tumiii!,' the inatniment tliroujjh :8o' of azimuth. 

Tlie total uuuil>er of meridiuii trani^itH obtained during the 
18 1636, including 77 of t)ie Moon'n lirnbis and 44 of the lu 
craUT MiisliDK A. The number of t-xtra-meridiau obHervatioiu 
the Mooii obtained during her fimt and la»t quarters 19 40. 

A new set of wiren was inserted in the iiistnimont in October, 
and in connection with the determination of Their intervals a 
•ietermtnatiou has been taade of tbe errors of the three anrews of 
Ri};ht Aftcoiision, PoUr Distflnco, and Position Micrometers. 
third of tbp.<«e microiueterB serves to readily connect the two t 
vitli each other, and thus ttimptifleA the determinatiDQ of 
errors. 

netfex Zeniik I'uie.— Durinj? the year, 1 1 70 double obserTUttoM 
ond 37 single ob(ier\-atioTi3 have been obtained, the brighter stum 
having been nbflervi-d iivor ra lon;^ periods an posttihle. y DracMi 
was observed on B3 days, /? DracoiuK on 56 days, 1* Ot/yni oa 41 
days, und fJrm' Muji/nf on 27 daya. 

Oeciiitaiions.- — D'lriiis the year 1 7 disappearancea and 6 
appearancea of titans occulted by the Moon have been observed 
one or more ubaervcrft. The rceult« have alrea*ly been cotnm 
oated to the Society. 

z8-tn«A Re/nicior.^A new working catalogue of dtrablf si*a 
ytoA brought into u»e in the course of 1906- This calalogu 
includea, as its niatn feature, tho double stars discovcrwl by Hoo, 
the remaining jiaim beicig B(!lei:ted from Struvc, Otto Struve, Bu 
ham, HuMst^y, and Aitken. The v-eiithi-r has not beon at 
favoiirablf* for duuble^^tur work, the long spells of non-obsemtto 
weather causing serinus interruptions in the progranime of ohserrA- 
tion. However, the 414 stars obeerved have been measured, 
the ftvcraf^e, on twi' night*. 

Ad analysis of the observations gives— 

Hough Starit. 

18 under 0*5 separation 
x8 between 05 and i"*© 

36 between i*o and 2"o 
165 over 2*o 

JUiscellaneout Stan, 

It 

37 nnder 0*5 separation 
45 between o"5 and i*'o 
37 between ro and 30 
j& ONet ro 



1 

uus 



feb. 1907. Sighty-tevenik Annual Otnerai Meting. 245 



PegaH was obflcrved on 14 nightA, S Kqrtu/ei on 9 ni;;litN, 
id 70 Opliineki on 1 1 nif;ht«. The lucusured of S EquiUei contirm 
|tkc tjiort (lenod (57 years). 

Tbe equatorial and polar diameters of Juptftr were measured 
[on 1 7 nights witli tho bililar micrnmetpr, and al»o with tbe 
Idonble-imoge. Tbe satellit^ft were mcaanred on 2 nigbla. Owing 
[ko the necossitj for renewing a portion of the wbeeNwork for 
[opening tbe Bbiittere of tbe dome, tbe 28-inch wa« ont of D«e from 
[June 37 to July 31. 

7'homptOH £guaiifriai. — With the 36-inch refractor 63 phut<>- 
ikphs of Neptune and ita satoHitc have been obtainoil on 24 

With tbe 30-incb reBcctor 24 photographs of J vi. were 
[obtained on 11 night« and 4 of J vii. on 3 ni^bta from January 
II to February 15. l.>aring the whole of chn 1905-6 op[N'<«itt<in 
l(froro 1905 Augiiiit 33 to 1906 Febrnary 15) 86 pliotoj^mpbR of 
\jvi. WL'Pi obtained on 36 uiKhta and 19 of J vit. an 15 nights. 
During tlie prn^iyiit opposition, up to December 31, 31 phoiojjniphB 
of J vi. hove been obtained on 16 nights, tbe serie« commeticing 
an August 28, and 6 photographs of J bH. on 4 nights (Nov- 
ember 17, 23, December to and 12). 

Pholograpbfl of cometa have been taken in the year 1906 ai 
follows : — 




Comet c 1905, 4 


photograpbd 


on 


4 nights. 


a 1906, 19 






14 „ 


b 1906, 30 






»5 .. 


d 1906, 31 






>9 « 


'T 1906, 7 






6 .. 


9 1906, 5 






5 » 



78 phulo^n^phs of 31 minor planeta bavu also been obtainod. 

These photographs were all taken for detorminatioii of jjosition, 

iMiotographs of the nobnlw, M. 51 Can, Vmh. (100"* and 60"'). 
M. 57 Lyrv (5"* to 20™), and M. 31 Andrumedui <ioo"), have a]«o 
been obtained. 

In addition, a few plintographa have been lokoa for ioBlru- 
mental ail,iu«tmentB. 

As regards tbe measurement of photographs and reduotioni 

The printing of the Eron measures iimi reduetiuiut is coi 
with the exeeption of the <litM:uB8iun of reNuIts, In the 
this discuBsion the errora of the ri^seau as p'tn-t' 
plat«8 have been discuiaed with upe^ii^l wftt^wt^ t 
ike determination of the »olar poral' 

Tbe photographs of Neptune ^i^' 
iliscuraed as far as the end of the lost 
published. 

Tbe pbotojs'rapbs of J vi. and J 
and of Comets 1903 <*, 1904 a, 1901 
1906 b, have been meaaurvd, and ti 




246 



Rejfort of iht Council to the 



LXVII.4. 



The measures of photographs of C^omets 1906 f/, i9o6e,u>l 
1906 tj are in liaiiJ. 

The iiiiuor plaiiets photographed in the ycsra 1903 snd 1904 
have been mtiiuiured, and the rmniltii published. Thom phot» 
graphed in 1905 nre ready for publictttion, and tho«e obwrnd 
in 1906 are in hand. 

Astrom-aphic Eiiuatwial.—Vi'ork with this iustruiueut has iliD 
mainly lieen confined lu rt*pla::ing chart ]>lnti>ii which, thoui*li »atii- 
fa*;tory in othijr retjpocta, are, tiwtng to slight phutojirapbic defwU, 
unfiuitable for production of enlarged prints. Duriug the yi»i 
133 chart platen, 4 catalogue plates, 22 plates of the field monij 
Jupiter, one of Mars, and one of Comet 1905 c were taken. Of tbc 
chart plates 30 were rejected, principally becatisc they did not mm 
up to the standard in shoving faint stars or for phutognpUe 
defects. 

Tlie measurement of the catalogue plates baa been complied 
by r«meiuturinL; the images showing discurdunccs in the Zones S5' 
tn the I'ole. The means of measurPR for thp«fl zones have beeo 
takpn and co[)y for pretts prepared. Thf^ printing of the meaaim* 
of Zones 80* to the Pole is practically finished, and the aecoD^ 
vuluine of mtiaiiuruK complete, with the exct:]ition of the Introdoc- 
tioa. In view of the large overlap of the plates immediatelt 
surrriiiniiing the I'ole, it woa thought advisable for the plates frooi 
declination Sj'' to the Pole to measure all the stars within the 
limits of the n^seau, and these measures have been printed on » 
difTenint system to tbotio of the lower zones, with reference namben 
showing aJl the plates on which each atar occure. The asaigDin^' 
and printing of these reference numheni hAs takf^n more time than 
was anticipated. 

Tbe L-omputation of the constants of the plates iu the seoood 
volume hns been begun during tbe year. Standard co-ordinatM 
deilmjeti front the places of the reference stars in the Greenwidi 
•Second Nine YearCatalogne, 1900, now in courBe of preparation, haw 
h<^n cnnipnted for the ptatoit nf the /.nnv.R declination 76' to 80' 
and 87" to tbe Pole, and the scale value and orientation coa«t 
computt'd for these platt-A, witli the exception of those of Zone 76I 

The counting of the chart platos (declination 64' to the Pol 
in now complete with tlie exception of a few fielda for which bott 
photographs will be obtained, 385 plates having been connt 
during the year. 

Kiilarged re])roduction3 of the chart plates have l>eeii made fof 
213 plates during the year. The total reproduced to Decembei 
31 i» 538, thn sis Zones 65^ to 70' being complete, and the Zone* 
71' to 74' nearly half liiiisiicd. 

Photolteli'jijraph. — Photographs of the Sun have be«n taken on 
209 days with the Thompson (9-inch) I'ltotoheliograph, and on 
6 dayii with the Dallmeyer (4-mch) during the time that tbe 
3o-inch mirror wan being resilvered, November 3-ta, when the 
Tliompson iiistrumeut was not available. (H the )ihoU>graph» 
Caicen, 576 have been ae\wAe4 \ot -ptwiKt^tfAfiii. Vtioto^raphs haw 



^ 




Teh. 1907. Eight^sevetUh Annual Gentral Meeting. 247 

^been recaired tbroagfa the SoUr Pbyncs Committee from Pehra 
NiD, Imlia, up to 1906 Xorember 27, aoJ these have been further 
supplemented hy pbotof*7Bpbfi from the Observatory at KodaikAnal, 
]n<lia, aod fn>Tn the Rojal Alfred Observatory, Mauritioi. The 
daily record thus made up is complete, witliout break, from 1905 
Janoary t to 1906 Xovomlier 27, the Jate of the la«l ludiau photo- 
lerapfa received. The last photograph n^ceive<l from KodaikAnal is 
dated 1906 September 13, and the tdsl from Mauritius 1906 March 
126. Tlio photographs from theAe tvo obeerratoriee have all beea 
[.nteasored ; thnM from Dehra Dfln have been meaanreH up to 1906 
[joly 2t, and thoM? taken at Greenwich to 1906 May 3S. The 
alar activity duriii}; the year has not been quite so great as iu the 
jrevious year, but the work of measurement and reduction rtiU 
>ntinu(« to be ver}' heavy. 
Concurrently with this, the preparation of the Supplementury 
Photoheliograpliic Re^-ults, 1874 to 1885, referrt-d to In tlie hist 
Aunual Keport, has been osrrieiJ on during the year, and is now 
approacliing completion. Mr Maunder, after ah intipt'ctinn of the 
plMtograpba stored at South Kenxiugton, found there 35 photo- 
graphs taken in Mauritius which filled 23 {.'ufw previoiuly exiatiug 
in the record for 1S78 and 1879, all of thesf- days being oocaaious 

»0n which tbe Hon showed spotit or faculfp, or ttoth. Theee have 
been lent to the observatory, and have been measured and rednoed, 
and the reeultu incorporat^rd with ttoee previously published in 
'^m the Greenwich volumes for those years, or by the Solar Physics 
B Committee. The ledgers of spot groups for the twelve years 
1S74-1885 have been paaaed for press; the daily projected areas 
have been computed for the entire purio<l ; and the computation of 

I the mean daily areas and meuu latitudes of the 8])0ts fur each 
rt^tation of the Sun and for each year alone requiree completion, 
and ix already iu hand. 
The I'hotoheliographic Resnlts for 1905 have been passed for 
preH!". 
Printing. — The copies ol the volume of Gret^nwich observations 
for 1903 were distributed in April 1906, tot;ctlier with the Kfw- 
Keduction of Groombridge'R Catalogue of Oircumpolar i^tars and 
the T>etermi nations of Longitude 1888-1902. The volume far 
1904 was distributed in November and December, with an 
Appendix — Meridian >^«nith Distnnccs of y Draeotu't with (ho 
Heflex Zenith Tube 1886-1899; ^^ ^^ Meteorological Bedur 
tions. Part tV., Temperature 1891-1905. 

The printing of the 1905 vulnme is nearly complctt^d, nni^ 
second volume of the Astrotitaphic Catalogue will fthortly bo 
for ilistrihution. Otli^r publications now in the prt^ss, and 
cnmplotion, are the Hetiographic Kenulta, 1874 to 18I 
Meaxurefl of Photographs of £roi for debemiinatdon • 
parallax. 




^^ 



248 Jt^oini 0/ tht Council to thi LXTa4. 



lioyal Obaeroaiortf, Cnpe of Qood Hope, 
(Director, Sir Dttuid GiU, S.C.B., H.M. AMrottomer.) 

The uew irAnitit cir<-le haa been in regular use throagbout tii< 
ycAT in ob«ervatioi)8 for the new Fundamenlal Catalogue, aoii in 
oertain vesearclieB on the magnitude correction in R.A. which uy 
subBequentlj mentioned. The Kepsold-Struvc method of oWm 
tion I1&8 lieen contItiU4;d without use of clockwork. ExperimuiU 
have been continued with the clock-driven wii-«>, and so loni; a» 
the eelf-rc^ilatint; motor preserves a nearly uniform rat« the evw 
apparatus and dilTerctititd gear work to |>erfcction, and the $w 
can be maintained iu perfect bisvcticit on the travelling win 
lliroughoul thy transit by prewing one or other of two keys, of 
which the action of one is to aroelerate, the other to retard the mt* 
of motion of the wire by 4 per cent. But unfortunately the titc 
of the motor vanes by quautities fully ^reat^r than 4 per cenL, 10 
that, until this variation of rate is currected, the perfection of 
liisection during the transit of a star cannot he maintained. It a 
proposed to substitute a weight4ri<>'en clockwork, siiuilar to that on 
tlie a^itrographie telescope. 

Tlie underground uzimuth niarka have retained their constancj 
(^ reliiitvo uzimuth in a r^markalil*' manner. 

The old non-revi-rnible transit circle wa^ employed in oompU-titi^ 
the observationA of the list of stars of which observations uvrv 
requested by Professor Boss, and of the miRcellane<)u« stars iteed 
in the determination of latitude iu couuection with the Geodetic 
Survey, and stare of which nccultations have l»een obeerveU. This 
work was completed by the beginning of August. Since tliat time 
a aeries of observations of selected sl&ra whose relative pusiiiooi 
have been accurately determJneil by lieltometfr measuronifut ho* 
been made in order to determine the amount of personality of ih« 
obsarverrt de|iending on nia^nitiidv. That is to say, a bright star 
having two uiuch fainter stant, the one preceding, tliu other follu«- 
ing it, is selected^ — all thnic stars having nearly the aamo declina- 
tion, and the fainter ^Uin situal-ed nearly symmetrically wiUi 
respoct to tlie brighter star. HcUometur obwrvationa of the 
position-angle au-i distance of the bright sua with rasprct t*i the 
fninttii' stare obviously determine the iCA. of the bright »tar 
relative to the fainter scars, free from personality depending on the 
magnitude of the stars or of the adoptcMl scale-value of tlie helio- 
meter. Thin relative R.A. so found is compared with the relative 
R.A. derived from the meridian nhser vat ions, with the eatiafactoct 
rueiult that the miignitiide corrections deriveil for Mr Power and 
Mr Pead with the old transit circle hy tneans of screen olieervm- 
tions are conBruied for stars from Ma^*. 4 to 8, whilst for tiM 
observers with the moving wire the magnitude correction is nearly 
zero. 

The following observationa have been secured with tha mondial 
instruments : — 



Feb. 1907. Eighty-seventh Annual General Meeting. 249 



Wieh the old 5f on- reversible Transit Circle : — 


Nnmber of transits 


. . 466s 


Determinatioos of Z.D. 


. 403a 


» 


coUimation 


93 


u 


level 


• *39 


n 


azimuth . 


249 


n 


run 


249 


n 


nailir 


230 


I* 


tlexure . 


II 


With the new Raversibifl Transit Circle ; — 




Number of tnmaita 


• 359« 


Detvnaiiiatious of Z.D. 


• 3<i27 


It 


collimntion by collimators 48 


It 


collimatirvn hy reflection 




and reversal 


41 


It 


level 


4-22 


»t 


OEinmtfa . 


' 389 


Observationa 


N. azimuth msrlc 


• 370 


» 


s. 


• 369 


Determinations 


{it run 


249 


•1 


niidir 


■ 301 


>t 


flexure . 


64 



38* 


6 


64 


7 


33 


4 


48 


S 



The following oppositions of the mtijnr planAts have been 
sbserved nith thti heliometer during the year: — 

Kc.otObi. lto.ofNi«l>ta 

Opposition of Neplnne (1905-6) 
„ Uranus 1906 

„ Saturn 1906 

„ Jupiter 1906 

The following heliomeler olworvaUons have been made duriuy 
the yi^ar iu connection with Llic triangulation of the coraparitiuii 
stars :^ 

Uranus 1903-5, Saturn 1900 

rNL'ptune 1905-S 
Mars 1905 .... 
Jiipitfr 1905 
Miscellaneous 
The triangiilatioti uf comparison stars for Mars 1905, with 135 
observationtit, is now cumplete. 212 obstirvBtions in distance and 
130 in position analv have been made in cocmectton with theubove- 
nientioniil determinations of magnitude-errors in KA. as observed 
with the trauKil circle. 

Thirl^'-one obwrvationn each of distance and position angle of 
the components of a Ccutauri liavo been made by Mr <I. M. Baldwin. 
Comet 1905 <• has h«eri nb-iprved on 9 night« and Comet Finlay 
iJ on 1 1 nights with the heliometer. 

* Inoluditig 30 obftcrt-ationi in 1905. 



toi 


obAervalions. 


. 86 


i> 


61 


ir 


»7 


t» 


. 87 


n 




250 



Report Qf the Cottneil to the 



trvu. 



At tlie request of DrT. BanBchiawicK, observations of the reJ 
positions tif tSaturii uiid Aj Aquarii were iubcIh on 4 niglits. 

Thirty-tlire« separati^ pbeuomeun of occaltaliwis have 
observed, viz. — 



l«tfW 



Disappearances of atare &t the dark limb . 
Reappearaucea „ „ 

Disap{iearaiicffit „ bright limb 

Di»a[>|<i!tiraDce of Saturn - 4 phetiomena . 



'4 

M 
t 

4 



hm 



Witli the astrugraphlc telescupo the following work bas ben 
accouiplished : — 



OafcripUon of Plkt*. 

Triple exposure Chart platea 
Single tixpoBure „ 

Catalogue plates, second sories 
Kapteyn areaa . 
Adjustment plateH . 
KxperiuiciilH with Cooke leDS 
Miscellaoeoua . 



No. o( 

PiKlM. 

10 

>4 

II 

10 

5 



So. at 

45 
10 

69 

28 



20 



DonOlontf 
JO" 



20" 

6™ 3» 20* 
various 



The " Knpteyn-areaa " plates were taken ot the roquMt of 
Professor ,\. C. Kapti-yn in cnniieotion with his scheme for lb? 
deterui nation of the parallaxes and proper motions of faint star^. 

During the your 185 Catalogue plaltia, L-tmtainiiig 103,396 s-tars 
incladjii^ 2167 utuudurd starii, have been uieasured, both in direct 
and reversed positiotiH of each plate; the standard stars beiiig 
measured in like raonner by each of the two obaerveri by whom 
the alternate zones of the plate are uieasured. iS plates nMOsared 
in former years have since bweu rejected. 

The total number of plates now measured is 10S6, contaiQing 
about 600,000 star-images, corresponding to over 250,000 differrat 
starK. 

The actual ntate of ths measurement on Dacember 31 is ai 
follows : — 





Nti. u( Pl«tea meiwuret 






Cutitad fur Pivol 


: 


Loat. 


1906. 


Dutag 
1906. 


OuUtandlnii;. 


B«fDn 


Durtos Q^ 
1^. 


«— 


-41' 


140 


4 


... 


140 


... 


^ 


-43 


144 


... 


... 


>44 


.— 


^ 


-43 


142 


... 


2 


"5 


»7 


"1 


-44 


<3i 


1 


12 


66 


58) 


I 1 


-45 


■3» 


2 


4 


19 


108 


3 


-46 


"3 


29 


2 


3 


HH 


38 


-47 


65 


73 


6 


a 


1 


67i 


-48 


25 


69 


50 


5 


... 


14 


-49 


1 


6 


"3 


1 


... 


••• 


-50 


2 


1 


>I7 


a 


t 


•*i 


-s> 








120 








*.* 



901 



.85 



426 



497 



27S 



i*3i 



feh. 1907. Eighty-gevenlh Annual General Meeting. 35 1 



I 



I 



The VictAria t«I(>jtcope hiu) been employed principally for the 
[et«rmination of the radioJ velurities of stnrs by mfans of spectra 
pbottjgraphtd vrilh thu 4-pnsin Bpectrograpli attached to the 24-iDc)t 
^telescope. The instrutneul wa» used on 113 nights fur spectro- 
lecopic work, and plint*>griiph(i nf 245 spectra were secured by 
Messrs Luiit and Simpeoii- 123 separate spectra have been 
ItneiAurHdj and the radial velocity conipiileil by M«B8r8 Lunt, 
Goatcher, and Baldwin ; Mr Simp^nti haji given much aasistance 
till the reductiona 

Mr Lunt has prepared a paper on " The presence uf Kuropium 
in Stars," for commiinination to the lloyal Society. 

The iS-incb visual telescope has been employed on 17 nights 
for ob3er>'ations of Coniet Finluy and Comet Metcalf, by Messrs 
Hough, Lunt, lialdwin, and Simpson. 

Daylight observations of the poitition-angle and distance of the 
components of a Contaiiri were made on 8 days by Meaara Baldwin 
'Wid lanes. 

The printing of the Cataloj^uo oE S560 Astrographic Standard 
BUrs has been completed, aod copiea forwarded to Greenwich for 
diatribution. 

The Cape General Catalogue for 1900, based on observationa 
vfith llif S-iuch transit circle during the ycarx 1900-0+, and con- 
taining 2798 zodiacal stars and all C.P.D. stars not fainter than 
8*5 mag. (except those of zone -42* to -50*) vliich are not 
previously contained in any catalogue of precision, haa been paw»d 
through prBsa, and copies have been fient to Greenwich for 
distribution. 

MuridJaii ohRcrvations 1900-04. The ontstanding sheets of this 
volunne, ctintaining the reanlta of meridian obsHrvations 1900-04, 
all reduced tu the equinox i9<oo, have been passed through prem 
and sent to Greenwich for distrihiitioii. V()l. x. pari 2 of the 
AanaU of the Cape ObatTvatorj*, containing researches by Mr Lunt 
gn the spectra of Silicon and Fluorine, has been issued. 

VoL lii. part 2, containing Mr Cookson's ubtierTaiions with the 
heliometer of the relative distanceii and position auglea of Jupiter's 
Sat^Uites. and his derivation from them of the mass of Jupiter and 
the i u equal it ies of thu Satvltiles, and vol. .\vi. part 3, containing 
^Ir de Sitter's tliNniRtion of the inclination and nodes of the orbits 
of Jupiter's Satellites from photographs taken at the Cape in the 
years 1 891, 1903, and 1904, have been delivered at Greenwich, and 
will be circulated at tho next aruiual distribution. Vol. ii. part 5, 
containing meridian obeervatioofl of the Sun, Mereurj", and Venus 
during the years 1884-92 ; vol. ii. part 6, containing thf re-sults of 
occultalionx of utar^ by the Moon during tho years 1896-1906 
and vol. viL part 1, coutainin;; heliometer oUiervutiuns of * 
major planots during the years 1897-1904, have been forwaided 
preaa. 

The Cape dty-numbera for 1908-9 have besn printed 
distribnted. 

The reductions of the meridian obsetvations with the 



252 



Report of the Cwncii to the 



UEVtt4. 



transit circlo an coitiplbte to lliu end of tbe year. The ranlta 
have been forwanled to Profesaor Bosa. The detnaud for «ri| 
completion of the ohaervatioiis of the Boss-stars has delayed Ukr 
redtictionti of ohservations mude with the new tmoBit circle. Tbc 
right Eutcvnsions of the latter have been complutely reduced toi 
examined to 1906 October 25. The corrected circle rvadiiiKS l»n 
beea derived ti> 1896 November 25, and tb'': reductions to appaicbl 
placu applied to 1905 Nuvember 23. Owiuk, however, to Uw 
absence nf Mr Cox in England, the examination of the N.P.l*. 
reductioiia haft fatten considerably in arrear. 

The Constanta for reduction of the Aatrograpbic Catalofoe 
plntos for the aooea -41', -42", and - 43* have been derirei 
an also those for 64 plates of tone -44* and for 19 plates nf 
lonc - 45*. 

The helloQieter observations of CDniets and of tbe conjunction oj 
Satara and h Aquarii have been coMipletivi uiid sent for pnblicatioa 
to the Aftronomisekft Narhrichten, The belioineter obserratiuH 
of Bot» of slara required for the determination of nia^itQ<i« 
perHunat equation in meridian obeerving have been eompletei; 
reduced, and a compunaun made with the transit circle reBtilt«. 

The records of the seitimo^taph have been regularly forirud«d 
to Professor Milne during' the year. A duplicate copy, at tiw 
request of the German Guvernment, is supptiad through the Coowi* 
General for Qermany, Cape Town, (or transmiHsiun to the centnl 
station fur the investigation of eai-tbquakea at Strassburg. 

The meteoroloKioal observations have, as usual, been oota- 
reunicated to the Me teorol ordeal Comndsaion, C&pe Town. 

Colonel Morris haa completed the reductions of the Geodetic 
Survey of the Tmusvaal aud Orange Biver Coluoy, and he will 
return to Kngland early in 1907. 

The ehniu of triungulntiun connecting the northern end of thf 
30th meridian arc in the Transviial with the existing triangiilatioo 
ill Uliode-si^ has been completed by Captain Qordon, R.EL, io 
course of the year. 

No repurla have been received from Dr Rubin tdnce ^Iny 1905 
in spite of the most urgeot rcquetits made to him both directly and 
through tlie AdminiBtrntor. 

From repoit£ obtained from Mr M'Caw, Dr Rubin's assistaaV 
it appeared that the triaugulation is caitipteted as far aa latiCQd* 
- 10* 30'. It has bfon found nectvjsary, for various reasonK, \a 
mispenrl operations for the present ; the assistaota have beea 
recalled, but Dr Rubin has not yet returned. Tbe observation^ « 
far as received, are almost completely reduced. 

Mr J. H. Baldwin, a research student in Astronomy frrai 
Melbourne University, arrived at the Observatory on July 18 fi» 
a six months' caiini*! of i^tiidy in practical Astronomy. Since bi* 
arrival he has devnted himself to tbe study of the eyetem ni 
a. Centauri, both visually and s[X'ctruflCopically, and has u«bt«d 
iu the general work of the Ueliometer and the Victoria Teleacop*. 

On the 20th February 1907 8ir David Gill will retire after 



■ Feb. 

H^ nnmni 



Feb. 1907. Eighty-aevmth Annual General Meeting, 253 



completing hig tirentjr-«ighth jbat of Mrvica as His M^esty's 
AstroDumer at the Cape. Mr S. 8. Hough, Chief Assi«tant, has beea 
nominated hy the Lorda Commissiotiera of the Adiuiralty as his 
BDCcaeaor. 



li/tyal Obtervatory, Etiinburgk. 
{DiTertoTy Prof. F, W, Dyaofi, Aaironomer 2ioyal/or Scotland.) 



I Meridian Circle. — Dunn;; the jear aeveral changes have been 
made in the instrument. The moat important of these ure the 
•ubstitotton of a spriiiK 8U!<peusiun near the pivobs (as in the 
ijreenwieh altazimuth) for the old method of counterpoieing, and 
the introduction of a recording micrometer for the transits. The 
new counterpoise, introduced early in the year, is quite satisfactory. 
The recording mieroinifber is only Just completed, and it is too soon 
to speak of its perfitniiance. These and some other minor altera- 
tiona, comhined with nnfavoumble w(>iither, have made the number 
of observations of zodiacal Btara during the year someirhat xmalL 
The number of traiivits and senitb distances observed during the 
year is 900. 

t$-incJt h^qttatf/rial. — The Office of Works in July built a plat- 
form round the lower part of the pillar of the instrument, to make 
the handling of the iiuttruraent mora easy and comfortable. The 
illuminations of the micrometer and circles have been rearranged, 
and the instrument got into adjustment for ohservatious of double 

t stars. Only a few obsf-rvations have as yet been secured. 
Speeirofeopie Ohaervation of the Rotaiian of the Sun. — All 
favDOnible occusiuns have been utilised, and 677 sets of observn- 
tiona made on 67 days. A few measurements have aUo been made 
of the distances of the solar lines from the telluric standards near 
the Sun's centre, for comparison with the means obtuiiied from 
similar measurements at opposite emis of a dinnieter. 

34-inch Rejiffctor. — Thta iiititrument has been arran^;ed for 
photographic determinations of the [>osition of nebula!- Only a 
few photographs have m yet been itbtuiuud ; and although it will 
protAbty be impossible to obtain many photographs, it in hoped 
lo put the inatrument to this work. 

CkUaiogve of Zodiacal Stars. — The observations have been 
reduced to ir)oo-o as fur as 1906 February, and a manuscript 
catalogue forwarded ro Sir I). Gill. In the task of overtaking the 
arrears of reduction, ussiatance receiv«d from the Government Grant 
Commiliee of the Koyal Society is gratefully acknuwleilged. The 
obaervatioiis for 1906 are reduced to meau place 1906*0. 

Henderson's Cat^ilo^ue for 1 840, re-reduced by Dr Halm, has 
bun published during the year. 

Seismographic ol)9ervation8 have been made conliuuoosly by 
Mr Heath, aud tho results commuuicated to the Committee of 
the British Association. 

>feteDrological ubservations have been regularly made. 



254 



R^ori of the Couneii to tlu 



LXm .4. 




Gamlsridgp. Obtertatory. {Direet&r, Sir if. 5. BaB.) 

I. Meridian Cirde. — Tbo rovisiou aod completion for pran nl 
the large volume of ineridiBn circle redulti^ 1S72-1900, menUoDt^ 
in last year'.i reiH>rt, was finished in September, and applicatioo 
for printiiif^ has been made to the Syndics of ibe UiiiTersitT Pm. 
In till' course of revision at the meridian circle of all the aioglf 
obitflr\'«,tion fitare published in the Cambridge A.U. Zone Catalogs, 
it happened in a considerable nnmber of cases that the &tar, rd 
wbi<.h a single observation appeared in the Zone Catalogue, cmU 
not >>e found in thf> place amigned to it. The question then arow^ 
Was the original observation erruneoua, or did it refer to a ttrj 
faint star only visible lu the instriiment on oxceptioniil nighU 
With great kindness, Pmfeseor Turner undertook to exitmine 
tbeite doubtful caftan on the Afttrographic Catalogaa platee taken 
Oxford which cover the Cambridge zone, very nearly oil 
difficulties bave thus bi;en cleared up, and the Cambridge Cotal 
has derived ^rcat advantage from this final revisiou b^* the aid 
tbo Oxford pbotogmphs. 

Ti)ward» the end of the yi>ar the observation of Gill's Zodiaotl 
Stars was resumed, and z8o litarit were observud on 9 nights, vitii 
the iiCL'eHsary ob^ervatioita uf ruiidnmeDtal stMPS Hiid inHtrumeitol 
errors. Tbe retluclions to mean place are nearly complet-e to data 

Mr Hartley has befiu in charge »f the meridian cirt^lr* thruughooi 
the year. 

3. SheepiJmr^ E'/iicUorial. — One hundred and twentyaevi 
plBtvti, each coiituinui^ four or more exposures, have boon U^en 
Mr Uinks during the year, tbe greater part of theu in continuati 
uf ch{> series for the determination of stellar parallax begun in 191 
The observation cif the faintftr stars of tlie working list tb 
Adopted ie pracLicuUy complete, and the reaulu for 10 slnrs an 
reduced and published by Mr Kussell (if. iV., I905 June. 1906 
Deci-ml'tT). The ohaervation of the brighter stars veas intvrruptfld 
by the failure of the spectall colour screen after a considenble 
number of pktes hiul been taken. A new form of acre«n was 
eoustriicted in experimental form In April, und the observation of 
bright FiUirEi huK now l>een resumed. The finished apparatus will 
be motintod early in 1907. 

An extensive new working list uf stars has bwu prepared, aod 
is incorporated with the old a» vacuuciue occur. Obeervalionn of 
iheee stars were l>cgun in April. 

Kfr F. J. M. Siratton (Isaac Newton Student) bas beeo occap» 
with iin investigation of the pro[ker motions of faint stars in 
Pleiades by comjiarisoti of early plutes taken at Graenwich a 
Uxford {kinilly lent by Urn Awtrouomer Royal and tht- Direc 
of the Oxfoiii University Observatory) with recent plales tak 
with ihe Sheepshanks telescope. 

Mr Ktratton has also undertaken a new reduction of Schlii 
observations of the Moon for comparison with Hayn's determinatioD 



04^ 



1 




Ammmi Gmtrai Jfahnf . as; 

>flf Ae Mooa^ fibmliM ud of tin xlwio pm phietl 
o<]lM«iag A. 

Mf H. K. TTiMiill hM eoBtmocd, at PriKMon, U.SJL. tka 
■■i iwlnction of pktes of tiw stotkr pormUiut anritiL 

> FUtim9 ZmMk TWuhojhi. ~ Mr Cooksoo hu cD&iittwit 
tfat 7«tf his ohoemUiOM with htn BoftUn^ MuiUi t*W- 
aeopcw Tb* ebaate ta Terr QofftToonblc to Um oUm of *>t><^•rv»tion 
ge yii o J for o detvrmia&tioD ol the kbomtioii constant, luid u baa 
beoa fmrad impoMible to gather eaougfa iDakrial in on« y«aT. The 
olaervatioa* have thereforo beeo axtvndml (>T«r miolbrr y««r. anti 
it a expected that the two years togetlier will provido the Ufceuwarv 
obaeftaltoDs. 

4. Baimetion 0/ Krot Phototprof^h*. — The formation u( a homo- 
genaoDi qratem of coniparisoa star placea iia» made good pragrwH 
aod ta approaching coiupletioa. 

An account of the results of iataroompari.ion nf puhlialtod Boriaa 
from different obaervau^ries bax been puliUiihml duhiig the yoar 
(if. A'., 1906 June, NoTcmbor). This showvd the nocewiity of 
supplementing the ptiblialieil iimterial with more ooni[)U)te tloUiit, iii 
which tbe resulte fruui individuiil pUtos nre kept ii«|)arat<v Ity 
tbe courtesy of the Directors conct-rneil, a ^nsat |Mirt nf thu rv*|uirwl 
information has heon ohtainM. 

Tbe individual obscrvHtiuns have been cullectvd in a canl 
civtalogue of about iS.ooo cards and 50,000 oiitrioM. •Syxtematio 
correctious have been dctcrinlnt-d ami iipjtliol (i) In I'a<Iu<'« all 
the ohftervations lo the same nyittom of fiLiidumental HtarH, and (a) 
to eliminate tbe very seriouH erron in the form of magnitude 
equation which affect the reeulte of Beveral obnervitturieii. 

Charts of all available ataro have beun fiintiitlMtd to tbn Lick 
Observatory, and the coni|)anBon stars lor the n>dURlinn of tbe 
Crosaley Reflector photogrnphs have been aelootwi front them. 
Closely approximate piaoeit of the eelected stars huvu beun com 
municated to Professor G. D. Perrine, in advance uf Ibe dL-linlUvn 
fomiatiou of tbe Rystem. 

One of the principal objeetA in the formatinri of tlin oIom) 
standard system of »l&n — to provide for llm niduoUon of tbe very 
numerous Crossley reflector platen with small nieojumblu Jlidd — is 
thus in a fair way lo \nj ac«<rmplisbed. Tbe sanio syilem will bo 
available for all other series in which it is not ponsibln or deairabla 
to oae bhe UoiU$ tie rep^re as staiulanls — «.{;, ibe Oxford and Cam* 
bridge series — and will also supply the placos of a uruat |iart of 
tbe stars naed as comparinu stars by the visual nbM<rven. A 
coofliderable mirabor, buwaver, of tbe visual oomimrifiori *ur« usod 
at Lick, Tcriua, and WasbitiKt/jn wers too faint tu be found o* 
the pfaoto^mpfaa hitherto mcaaored ami published. Th'> p\»rjm 
«U tluae fltara wtn laarked 00 th« efaarta aapplx'd u. Lick, 
moit ti Ikan kavo ha«« idaotiAad Md seaMUwl on tb« C#f 
ptataa. TUi laakaa good a sariotu dafteisncy in tha prapar 
fot a sencnl redaetiaa of all Rraa obasrvat io iw. 

Mr Hinka has beco abUd in thia work tltfM^oul tJw > 



256 



Report of the Counrnt to the 



LXVn.4, 



Mise JtUia Bell, and aitice April Mr H. K. Ilowd hiM been eiigft^ 
upon the card cntalogue. The expoiiae of this assistance has beea 
defrayed by a grant from tbe Ciuvertimeut Gr&Dt Fund of thti 
Royal .Suciety. 

5. Iiuttruriuitt. — Courstrt of instruction in practical astrooomT, 
and in Held astronomy and surveying, have been given by Xlt 
Hiaks during tbu year. 



The A'ewo// Tekfcope, Cambridge ObtensUury. 
{Mr H. F. iV«K«/;.) 

The post year, 1906, was spent, so fur as new observationil 
work i« c(»nc6rnfid, in making spertroficopii: obserrauona of th* 
Sun, The woric wiia mainly directed tc dectdiag, by obaarvmtioiii 
of sun-yput specLni and other eular features, whether the conditiuU 
of atmosphere over the flat plains of Cambridgoshiro would jiisUfy 
a Bpecial outfit for nolar work. 

Tn the tirst half of the year the a5-inch equatorial was u^ 
with a liitfraction dpectri>;,'raph attached to it. In the latter ball 
u fixud hurlxontul teloacop!; was impruviscd by dismouuling the 
25-iuch object-glass and tixing it in a Htout wooden frame, witli it« 
axifi harizontal, at a height of about 6 feet aboT« the ground. 
Kunlight wan directed into it by means of 11 cadcisiat and aa 
auxiliary mirror. The Sun'n image was examined with a veiy 
powerful grating "pectroaeope. 

The result of the triids iti c^impletely deoiBive. ObwrvaUou 
with the equatorial eqiiipnient prove that good conditioiu of 
observing are available betweeiii 6 and 9 a.iu. Obaervations with 
the horizoutjii equipmcut uliow that the^e conditioiu are noi 
seriously impaired by bringing the tieam nearer to the ground. 

A short lu-uoujit of the obstrvutions and of some of the more 
rotidily derivable i'f.^ult8 has been coinmunicated to the Society 
{M. A'., current volume, p. r58). 

A |K>rmaDent horizontal equipment for wlar work is now in 
prnceas of const ruction ; the exiwnise of it is ti> be oiut by ui 
appropriation from the McCleiin bequeat. The new grating 8pt?etft>- 
Bcope of Littrow form, with collimatorcannera 14 feet long, mi 
set up in position in the north annex on December zi. 

Th<; measurement and reduction of stellar apootrm has bc«o 
carried ^itj during (he year. 

Jlryan Cookson, M.A., Trinity College, has been appuintal 
A&nii^tant in A-^trojth^'HicK, a new post with this title having beeo 
recently created. 

Mr J. H. Kubrecht, tcseureh student in astrophysic^ is in- 
vestigatini; the rcttation of the Sun by a epectroBi^opic method. 

Mr W. 11. Manning ft»aiata in the stellar work, and Mr L 
Stanley in the solar work. 



Feb. 1907. Si^tf- mvemU Animal GtMnl Uttiing. 257 



I 



Dttmsink Obeervatory, 
{Dindw, Frof. E. T, VHiUiaker, B^^al Attronamer c/ IrtlamL) 

Profesaor C. J. Jolj, who bad hold iho office of Royal 
Astronomer <A Ireland Aince 1897, died in January. Mr E. T. 
Whittaker wan appoint«d his successor, the ajipointitient dating 
from July i ; daring the first half of the year tlit< obHervatory wax 
in the charge of Mr 0- Martin, AssiAtAiit AAtnmnmer. 

Mr. J. W. Vice entered into reaideuce ailjoining the o^werra- 
tory Id September as a student o( Practical Astronomy, under a 
acbome sanctioned by the Board of the University of Dublin. 

The chief work of the year haA consifltad in the nbMrTalion and 
reduction .of the etare in the list of red stars — a >vork which waa 
commenced by the lale Director shortly twfure his death. The 
ol<8crTatioo^ which were nisdo with the Pintorand Mnriins tniridian 
circlp, are now practically completed, and the work of reiluctinn is in 
a forward stale. 

Tiie time service to Dublin has been continued as in previous 
years. 

I'be mirror of the Koberts photogrnphtc reflector was rostlvored 
at the obiervatory »t the beginning of D.>cember, but weather 
conditions prevented the use of this instruuiBnt during the rent of 
the month. 

The professorial courses of lecturer delivered in Dublin by the 
Diroctiir have been entitled "Theory of Optical Instrumenta " and 
"Theory of Knerg^' and Radiation." Domoustratiouis in PracliCMl 
Astrouuuiy are }^iven at the observatory by the A»!ii>tlaut Af^trouo- 
mer, and tlio South Ktiuatnrial bus been eni]>](iyed on the first 
Saturday in each month in showing objeots of iiitetttst tii vidittirs. 



Glattffow Obaervafory. _ {Direeior, Prof, L, Ovker.) 

The Director and bia assistant wure principully occupied during 
the year with tho reductiuna uf obser^'atioos obtatuod in former 
years. A paper entitled "The distribution of blue and violet light 
in the Corona »n 7905 August 30, as derived frnm photOL'ruphs 
taken at Kalaa>es-Sonam, Tunisia," has been accepted for publica- 
tion by the Joint Pi.-reimiient EolipKe Coaimttteo (of tlie lioyal 
Society and Royal Astroniiraical Society). 

The spectroscope attached to the zo-inch reflector was usei' 
19 nighta in the first quarter of the year. The otwervaiionr 
then discontinued, as Kome neccsiiary alterations had to be t 
The ^fticiency of the appiinitus ha.i lieen enbaiired by a o 
holder, which, being curved to the fociil turfucq of the 
makee it poasibiB to photograph with perfect delinition the 
between wave-tengths 6000 and 3200. The Hlmholdnrj 
on a micrometer slide, and its position can be adjuated or 
Ime. 



25$ 



Report of the Council to the 



Lxrn.4, 



< 



The obaervatioos of aUra close to the pole were taken up again 
after a year's iiiterruptiou. 

The scheme fur the removal of the observatoiy has not y*A 
taken ileflnitc sbajio. 

Thf^ time service and the nielooro logical obsor^'ations have berft 
carried on as in former years. 



Liverpool Ohmrvatory. (Director, Mr W. E. Plwnmer.) 

'Ilie equatorial ban been iiRerl mainly for the obserration of 
comets, a class of observation with which this obscrvalorj hv 
becDiUL' idunlified. Tbe observations, fully redoced up to the 
middle of the year, hove been communicated to the Society aQ<) 
printed in their Joumalri. TltB observations of double stars barv 
alao been coiitiuuetl. During the last year some systematic 
inquiries have been made with the view of detecting, if possible^ 
the effect of aperture ftud fticul length on the measure*. For 
thin purpose attempU have been made to determine the orbits of 
aomd of the longer known binaries from observationa, limited ai 
closely a(t ]iD.<)5iI)tK to Uie Home aperture. It was thougbt thit 
somo of Um vartuliona frum thctvry might be expluined as due to 
the employment of larger teleBCopen than formerly. This work it 
still in progress. 

In other departments there has been no alteration durujf; tbe 
year. The meteorological and Koiainolo^ical observations are con- 
tinuously maintaint-'d. Scisrao|,jram8 uf the more remarkable earth- 
(];uakefl have been forwardnd to tlie anihorities who are diseasing 
particular effects. The testing and rating of chnmometera and the 
exHminiitioti of other at^pamtuii formtt pari of the routine worit 
of tlie ubaerviitory. I^ctiirffi, in connection with tbe Univeraity of 
Liverpool^ are regularly given u* the observatory. 



1 



Itotiflijff Ohmrvnfonj. Oxford. 
{Director, Dr A. A. Rambanl, Ha/Mife Oh$erver.) 






The principal astronomical work of thia observatory during tbe 
year 1906 has consisted of itivestiRations of stellar parallax carried on 
with tlic 24-incb photographic ut[uuturtal according to the method 
advocated by TrofeaBor J. C. Kapteyn (Itudetin de la Cartt tin OUi, 
tome i. p. 3^2). It will be remembered that his method requims 
that a piatv shotdd be exposed at least three times to the same 
group uf Hiara ut about the upochii of maximuuj purnllactic effect, 
the pointing of the telescope b^•ill^.■ slightly different on tho thm 
occasions, and the relative paratliixea of all th>e atara on the plate 
_are deduced from measures of tbe distances between the images of 
:h stsr so obtained. 
Thu plates employed for this purpose at thuRadcliffe Obsorvatory 
are of tha same size as thoae used in the astrogrsphio telescopes 



Feb. 1907. EiyhtyseteiUh Annv^l General Meeting. 259 



riz, 160 mra. x 160 mm., but on account of the greater focal length 
of the Oxford t«lt!scu[)u (33 fU 6 iti.) they cover ouly on&^uarter 
of tbu arci) of the sky takeu in by tho former. Exposures nre 
given of such a length a!> will in each oofie bring up at least 100 
^^tera on the plata. 

The rc-gioDH observed thia year barn for guidiug stars which are 
ttpproxiuiatbly central the following objects : — 



No. of FUt«t 
AxpoMdfor 



B.b. No. tkatcrlpUon. T«)« Ko. KA. tQos-o. V.P.D. 1905-0. Mac- 



I I 



+25. 49S 

+41. 750 
+ 15. 65' 
+ 51, 1094 
+ 44, 1408 

+ 40. i7SS 
1-48. 1469 
+ 31, 1684 



LhI. 3761 40 

Nutra Persfii 43 
UL6J;S8-9|>r. 44 
lu Hyula 
Dr. 990 



Lai. 13.427 

1^1. IS. 390 



5' 



57 
61 



It m • 
3 2 4997 
3 24 44-30 

3 40 32-63 

4 29 10-01 

5 30 47 '39 

6 9 55-05 
6 49 51 -08 

6 54 32'S6 

7 47 39 '02 



64 o 43-7 
46 a; 14 '6 
4S 50 10 'O 

74 41 33"l 
38 36 565 
45 15 16-6 

49 47 32 '3 

41 aS 3S7 

59 6 5-4 



7 9 

8 a 

8-5 

7.9 

8-4 
8-6 
8 a 

S-3 



Six of the$e objects are included in the list of atars vho«e 
parallaxea have been determined with the Yale helionieter 
(Tranioctiom of the AtftrtfTtomicul Ob»en'atory of Yait L'mvertiiy^ 
pt ii., vol. I. p. 196). Their cumbers in chat list are givtsn iu 
the third uolumn of the above table. To this list of objects should 
be ftddL'd 6 c Cygni, which has been included in the Oxford pro- 
graaime as much for the .sake uf alTorditig a check on the accuracy 
of th« mrtthudfl udo[ittid an for ilie purpose of obt.iining a fre«h 
value to add to the already numerous deteriniDabiong of the 
parall»x of this Htar. 

On thiMe objects 63 plates have been exposed during the year, 
representing 313 exposures. All photographs were tak^n near the 
meridian, and as uear the e]>oclis of maximum parallax factor aa 
possible. These two conditions necessitated the taking of the 
obaeivations at one season (January to April) in the early evening, 
and at the other {September to December) in the early morning, 
houra. 

The last three columns of the table, showing tho number of 
plates exposed at one, two, or three eeeisons, exhibit the state of 
this work at present. 

Arrangements are now being made to bring this parallax inveetigft- 
tion to a conclusion, and %o employ the 34<incli tole»cope iu tho future 
for determining tho proper motion of faint stare down to the 14th 

Jk magnitmle, in accordance with Professor Kapteyn'A schema, entitlet^ 

I " Plan of Selcctyd Areas." 

I A number of plates other thau those taken for parallax ha 



360 



lUport of the Couiuil to the 



LXrai 



beeu obtained in the oonne of tbe ytait. These ioclode p^oto- 
gnpbs of Brooks' Comet, the gnat K«bnla in Orion, the Pleuide^ 
Prwep*, th» gmt Clusteri in Peneai, the GlobaUr Clostflr (13 H) 
in Hercole*. the rej^on around the nor^ pole, etc 

He new RadcliSe Catalogue, cuotaioii^ places of 177a aUt^ 
fortbeei>och 1900, wu published ud distnbiit«d cAriy io tbe^^sf. 
For mmtj ye&n put the revtsiuD of Main's obaerrations made wttk 
the transit circle during the Tears 1862-1876, and pabltsbed a 
vols. xxii. to xxJEvi. of the Radcliffe Obeemuions, has been i*ppgpi | 
the BtteutUm of H^rr Haii^ Osten of Bremen, id coanactioD viti 
Dr Ristenport's Gejvfiu-hl^^ de* FiigtrmJiimmele, Herr Oita 
has volaot&rilv offered bt« Memcee for thts worl:, at>d baa hitbefV 
carried it on entirely at his own expense. At Dr Ktetenpait^ 
request, the original recor^ have in numerous cases been examtoci 
at the BadcliSe Obaervatory, and many discrepanetea bare tkai 
been removed. Tlie work is tiuw ap|>roaching compleUon, and it a 
hoped Ibal the publicatiou in the form of a collated oacalogoe it 
Main's results may not be much lungtfr deUyi-d. 

The preparation of another meteorological Tolame has eB|;ipd 
the attention of the staff for a cousiderahle part of the year. Tkui 
volume, wbich will contain the results of observations made in tk 
years 1900 to 1905 inclusive, is already well advanced. 

Mrteorological and earth temperature observaLiuns have baa 
regularly carried on as heretofore. 



tJnivenitt/ Obaervatorjt, Oi^ord, 
{Director, Proftsgor H. H. Tmmar,) 

The energies of the staff have been abnost whollj ahsorM 
during the pa.st year by the heavy work of proof readings and t 
certain amount of revision, involved in pasdog two votumes of th* 
Atiro'jraphir Cntnlcffue through the press. Vol. i., coataini^ 
measures of 6^,750 st«Usrimageft on the 160 plates, with centra 
in Zone +31 , bas been iMued to a number of observatories, axM) 
vol. ii. (66,718 images; 160 plates; Zone +30*) is in the bioder't 
bauds. VoL iii. is begun, and iv.-vii. will, it is hoped, follow at tht 
rate of two per year ; vol. viii. being reserved for discussions, etc. 



tb 



TempU Obtervahry, Bughy. {Direetor^ O, M. Smln-okc) 

^* "Die jwincipal object in the erection of this obaervatory wu ih* 

^og of a taste for astronomy in the school, snd its us« for thit 

"^^^^'^'^e incrsasea, and not much time is loft for other work. A 

are aedu.,^^pgj of doublestars have, however, been made. On cloudr 

Th**'^!^ boys are taught to read verniers, to set the transit snil 

1 al, and io take transits and measure donble^tara, uang 

of the t-tars for these purposes. 



FeU I5^7> Eighty-seventh Annual Oetural Mteiiiuf. 26 1 



Solar Physic* Obeervaiory, South Kenein^/ttm. 
(Director, Sir Nonnan Lockyer, K.O.B.) 

Observations of Sun-spot Spectra. — Tha Sun was seen on 253 
dnys during 1906. urid observations of Sun-spot spectra wero made 
on 132 days, permitting the exnmination nf 325 spots id tbe region 
F-W The reconln cantinuo to indicate that the lines afTecied are 
due to Viinadium, Titauium, ScaQdiuni, and some unknown element 
or elements. Daily )j]nitt>j;ra|ili9 (glass iieyativts) of the Suu'b 
disc are received from Dehra Di^n (India) aii<l MaiiritiiiR, the gaps 
HI the Indian record heitik; lllled up ha far as ]ioiiitible by negatives 
from Mauritius and Greenwich. The negBlivea are forwai^ed to 
tiieeowich for uieasurenieiil uud reduction as they are required. 
^'^DrittWi on paper arc also received ; these are mounted on cartridge 
paper and bound up into half-yearly vohimes fur ready reference. 

Speriro-heliograpk. — 1'he wpatlier condicluns were eoDiewhat 
better than iluniig 1905, buiu^ fine enough oq 163 days to warrant 
attempts beinj; made to obtain mouocbn^nmtic phuUigrapha of the 
Sun ia *'K" light. The in&tniinnnt cannot be used aatififactOTJlj 
during the winter months on account of its position among high 
buildings. During the puriud 1906 January 37 tu Decemlwr i 
390 negativea were secured, showing the diHtributiou of "K" 
radiation on the ^xxn'». diAc ; with the addition of an occulting disc 
over the primary f<lit plate, 95 negatives were obtained, showing 
the prominences round the solar limb. 

By arrungi-'meut with tbe Indian authorities, photographH taken 
with tbe speciro-heli'igmphs at .South Kensington iind Kndnik^nal 
are exchanged, so that the records may be aa complete as possible 
for the year. 

Stellar Spertra. — The wtathur conditions for night obucrvations 
have been extremtly unfdvnurablf? duritii; the greater part of the 
year. The new mounting of the 6-inch Fleury prismattr. camera 
has been a great improvement, and th** tUi^turb^inces showing as 
declination steps appear to have been eliminated. Porty-eight 
photographs of nint-'teeii stellar spectra hiive been obtained with 
the two |>ri'<ni» ; twelve stellar spuctra with the ^-iiich prismatic 
reflector ; the 2-incii quarts- cal'rite prismatic camera has been 
employed in photographing ten pnirs of stellar spectra, under 
conditions as nearly constant as possible, for recording extensions 
of the coutinuoue spt^ctrum iu relation to the |K>sitiDns of tbe stars 
on the temperature lurve of" chemical classificfltion. With the 
36-tnch retlf-ctor |ihot*>grapliH were taken of the »[)ectrum of tbe 
Orion nobuhi, o Cell (Mira), and a Oiionis. 

Publication. — Various papers dualiiig with stars of peculiar 
spectra, hftrometrie variations of l'>ng duration over large areas, 
wave-lengths of enhanced lines, mid ecUpae reductions have been 
completed during the year, and others on allied subjects are in 
course of preparation. 



262 



Report of tk« Council to the 



Liva.4, 



Royal Colleg« of Setenee^ South K«neington. 
(Agsietant, Profeesor A. Foteler.) 

Tbe ob0cr%'atory exists primarily for Uie instruction of atodaif 
but same of the iitstniiiietitft are alao employed in tbe spectroMC^ 
exaniiimtiou of .Sun-spots and prominences. Solar obeervfttiou 
were made on loo Jays during Llie year. 

Tiivi<tiU;{:il)i!ii»t of terretttrial upi^ctru are also carried an, iwin 
particularly as regards their applicatiou to tbe interj>retation of 
Bolar pheauuicna. Some of tho n.'!iulta liavo beeu published in ttie 
Mouthy iVoiiceg (vol. Ixvi. No. 6), and in tlie TranfiaeUioiu </ the 
ffUeriiational Solar Union (vol. i,). 

Stonyhuni Collei/e Obaervatary, Aetrophyeical D^ariment. 
{DirtctoTy Rev. W. SUgreavu.) 

The Bolar tturface has been under ohscrration on all availablf 
Ittqfs during the year, and 210 drawings of spots and faculje bsvr 
been made. 

The large grating spectrometer has tlao beeu employed npoi 
the larger spoU when the atmosphere has been calm enough for 
the steadv worlciiii; of the jvretient helioatat. 

A now helioatat \& being bnilt for the observatory by Sir 
Howard Onibb, thruu;{h favour of the Royal Society's OavemmeLt 
Qrunt Committeo. This will carry a 1 2-iiich silver-OD-gloas reflector, 
on loan to the observatory by the British Astronomical Asaociatioo ; 
and the system will be completed by a second refiector of 16 iucbw 
dinmoter, lent hy the Royal Astr[>nomical Society. 

With this addition the full a[>erture of tbe 3-iacli objective ol 
the uld equatorial telescope will take the place of the preaent half- 
filled 4-inch lens, and ih expocti'^d to add very gretttly to the 
efficient working' of the largo Rowland grating on the solar aurfaoo. 

The 4-inch prismatic camera has been employed on almost 
every available night, hat only on a tiolected number of th« 
brighter stars which bad been suspected of showing voriablf 
spectra. 

Some very good photo- spectrographs of Mira Ceti were obUitied 
between N'ov«iiibHr 25 and j>inuar>' 3, tnth by the Hilger compound 
prism adapted to tha great equatorial, and by the Thorp objectiTt 
prism on the Cook 4-inch Finder, nuw mounted aa a separate 
equatorial tele«cope. Hut the hopelew clouds and fogs of JanoaiJ 
have shut out all possibility of following the star's spectrum throng 
tbe conditions of its declining light. 



Wolsiwjham Obtervatory. {Rev. T, E. E$pin.') 

The work of mBaturiug with the micrometer n^lected ddil 
stars, more especially those of Sir John LIcrschel, has been ooa- 
tiiioed in the i>a8t yt-ar, and the results presented to the Society. 
During the year 134 new pairs have been detected and measiind. 
Observations were made on 70 nights during the year. 



Eighty-seventh Annual General Afeeling, 263 



Sir William I/ugt/itu?8 Obserrtatort/, Uiiper TtUae Hill. 

The photogmpliy cf the spectra of ^tars aud of other celestial 
iaa, wtiioh has been in progress for many years, is being 
ilinuad. 

Kxperiinijiila] wurk in the laliuratnry hiut iooludwl further 
experimiintH on the radiation of radiiuo, of which some 0/ tha 
I tesult.'f have appeared in the ProceedingB of tlie Royfd Society. 



5i> Wilfrid P^k's Obttcrtniory, liousdon, Lyme litifiis. 

{C. Gromr, Ot$ervsr in Charge.) 

The ohservaiory and astronomical instruments are in good 
workinjj; order. Weather was favi)urublt<, nnd observations were 
made oil 148 nighte during the year 1906. Oliscrvatiotiti uf the 
lonp-period variable stars have beeft continued on Argela:ider'fl 
methoi], and 407 magnitude determinations ivere made ; 18 maxima 
and 4 minimn have been recorded. During the twenty-one yean 
thin work has been in progress 9707 magnitude determinaticiuii 
have beuu made, aud 379 tnaxima and 288 minima have buen 
recorded. 

Several of the comets of the year were observed ; they were 
motitly ver)- faint and of little interest. 

The planut Batuni was favourably placed duriuff the autumn ; 
and September being remarkably fine, with twenty-three nights* 
observation, the smaller AatetUt^s were better seen than usual, and 
several interesting configurations were obaerred. 

Tha minor planet Ve8ta was obaerved on several nights in 
Kovember. It was «asi]y seen with & binocular glass, and its 
motion followed from night to night iu the vicinity of the weU* 
icnown doublo star 94 Aquarii. 

TranKits of stars for regulating the si<lereal clock were mostly 
taken during daylight. 



Mr SasndtB^g Obtavatory, Orotetltome^ Berks. 

The measares of 1800 points on a Verkes negative of the Moou 
taken 1901 November have been completed. About a quarter of 
the wurk of reduction has been accomplished. Rather more than 
1500 points have been partly measured on another Yerkes negative 
t^en 1901 August. Of these, 400 have been completely measured, 
the plate constants have been determined, and about too points have 
been completely reduced. The constants of both theHu pliit«a have 
been determine^i by Prnfeiwor Turner's methtxl (J/. N., vol. Ix. pp. 
302-305), ^^^ ^^^ pmhable errors indicate that a satiKfactory 

I degree of accuracy has been attained. 
■ 



* 



2^4 



Report of the Cimncii to tht 



LXVIL4. 



JJr W. K. Wit^oiif Oh$ervaiory, Daratnona, Co. Wealme^tth. 

The long (leriod of cloudy, wet weather stiemg to hold, ft&ia Wl 
oil 251 days, liiviuy a total uf 35'8o incbcis. Practically no work 
was done in the obsurvatorj*. Tho experiments were coDtioned 
with the new inBtrnment, which has been named a Badio-Integntot 
This simple int<Lrumi-nt gives the daily amount of the Tertical con- 
ponent of i^olar radiation in naloriRx. It ban been adopted at Kr«. 
Falmouth, AbcrdeeD, and Valentia. 



Ko'-laikinttl and Mndrtu Obaervaiortcf. 
{/Jirfidor, C. Miehif Smith.) 

The first live tnoutlis of the year werti, on the whole, favourahk 
for solar ubservatiutis, hut the remainder of the year waa decidevjlr 
unfavourablo. Thero wore 26 days in the year on which » 
observations were poaaible. 

PhotohfUoijravtx were taken on 317 days, uid approximita 
positions of spots were obtained by projection or by oye ohserntiool 
on 339 days. Up to the end of NovemlKr it was found poAsible to 
send to Greenwich all the i^olar ucgatlves required to fill in tbi 
gajifi in thr* Greenwich and Dehra Diin fiet of daily photograph*- 
In all, 297 new groups of spots were recorded during the yeti. 
The mean daily imrnlwr ol groups viiiiible Tarie<l from 1 'S ia October 
to 7'2 ill July, and tbu average for the year was 4*4. 

Spectrofcopic wwrfr.— Oljservations of spot spectra were madeoa 
181 day^, and prominences were recorded on 269 days. It has not 
yet been possible to begin phologi-aphic work on sun-epot spectra, but 
tut Mr Evenihud is expe^^ted to join the stufT early in 1907, this defect 
should snou be remedied. The necestary apparatus is available, and 
the only difliculCy is to find the time rei|uired for the work. 

Sjjedrohsliofjrapk. — Photographs with the siicctrobeliograp)) 
were taken on 277 days. The tntal number of plates taken ww 
1163, but of these a considemble number ttad to be rejccteil h: 
various reusoni?. Mottt of the failures were due lo attempts to 
obtain photographs through clouds or in short breaks, a few weit 
due to bad "etting, ami a few to dnfective plates. The inirtnimonl 
has worked admimbly during tho year, and a large number at 
excellent photographs both of Hocculi and prouiineocea have beeu 
obtained. Trouble froio unHtGaditiesa of the air baa, of coarsi^ 
continued, but it has been considerably reduced, and it is hoped 
that when the new building for the sideroatat, now nnder roo- 
stmction, is completed, still less trouble will be experienced frtun 
this source. 

Publirations. — Bulletins No«. iv. to vii. were published daria| 
the year, and Nn. viii. was in type at the close of the year. 

At Madras, astronomical obserrations were conBnad to ihom 
necessary for the time service, which was eflicicntly wainUuoed. 
A now KieQer clock has come into use, and bos been fount 
aatixfactory. 



[Teb. 1907. Siifhty-Kmnth Anrntal General Meeting. 265 

At/A OI'Merivitor'/, Westem Aiiffratia. 
{Director, Mr \V. ErtK*t Cooke.) 

AfUrotpraphic, — Diiriug the year, 167 plates were lakea and 
liH satiiifiictory. In addition, 21 ['lAtCA luive been exposed 
inot yet ileveloped, owing to the destruction of the rt^eau, Hther 
growth or chemicnl iiction, first Doticed on 1906 December 7. 
new r^seau ha>t been ordered, and upon it« arrival the plate k which 
/e been already exposed in the telcacope will be completed. 
There atv now only 101 re^ona t4j bu pliotograplied, aad these 
► urili prnbably be finished by Jwly. 

Nt) priDviiiiDii has yet been tniule for meaMnriug the plnteft, but 
rearraii^'emeota of some kind will prolmbly be made ithortly, owing 
t<i thi' crt-atiun of u Fei.1erul Wmther Burt^au, aud it is hopud that 
the pressing need for this work will then I>n recognised by the 
Government. 

Transit Circle. — 'Vhe whole year haa been devoted to the 
I observatiuii and n-duclion of tbo 430 sc-condary standardit which 
ftre to b« used as fundamental stare for the zones 31'- 41' S. declina- 
tion. The obAervations are completRil, and the catalogae will tte 
ready for the printer in a few <lays. A niinitnum of 10 complete 
detenniiiatioiiB of nearly all the titers has been secured, and the 
Catalogue, it is fauped, will be pnuted and distributed very shortly. 
' The following is the result of the year's work in tabular form : — 

Nights on which tim^ was determined . 310 

ObservatiuDS of secuudary atandarils in R.A. . 2718 

N.P.D. . 37j8 

ObservalionB of clock stars in R.A. . .991 

Collimakion error . 25 

Separate determiuatioDH of ^"^t^' '. 1" 

Nadir point 118 

Headings of meridian mark 136 

Mtieorolotjical. — The usual meteorolo^uol work waa ooutittued, 
and the annual report for 1905 printed ami distributeil. The new 
method of isMiin^ forecasts has proved very auccessfol. 

The Federal Parliament auLlmrised the creation vl a Federal 
Weather Bureau, and Mr H. A. Hunt, of the Sydney Observatory, 
been appointed Fetleral Mel*^orolo^itit. The "^JU 

ibly come into operation durtni; the present 



Sydnaij OhnensUory. (Acting DincUi 

Early in Januury 1906 Dr A] 
Lieutenant of Ui>ii Italian M^'esty^a f 
and at this ohwrvatory, in the sanr 
obBerrars, undertook a series of g* 
nhip rcmainud in port. At the F 
took magnetic observations on 



266 



Jieport of the Council to tfie 



LXyXL^ 



I>r Ht^kor of Potarfam in the year 1904. The computalioD* an 
not rediic(!(I yet. Inn Dr Ale^io hax hopes that they wiU compan 
favourably with thoso of previous nhservers. 

Another officer, connectej with the Carnegie Scientific rDn«ti' 
Rations, Mr G. Hviiuhrod, visited Auiflmlia 10 November 1006 l^f 
magiiftii.^ detfMiiiinntiona, ami has, in N. S. Wales, nst.-d the **»' 
position and pitr at thu Ked Hill BniDt:b uf ih« Sydney ObserralotTr. 
80 that he may be able tti verify the previous cuiupu tat ions, 

A& KtaUd in the liittt report, it van found necessary to tMOtm 
the magnetic inatruments out of the inBueuce of the el*«ctric fts^nj 
now fu) iiiucli itsed for municipal lighting and tlie tramway !-:vtvi<:' 
The magnetic work is now done at the Ked Hill Branch by Mj 
Short, l-he attirunooiical photographer, in addition to his duliA* is 
uetra photography . 

The i]itH:hanician, Mr W. I. Masters, has, as opportunity 
occurred, practically remade aomo of the lnfttrum.ont« in uk to 
many years The ta}ie chron'^apb, prooQied prior to 1S65, and 
wliich had 88 lbs. to drive it, is now a new iustrunieul, and il 
driven by 30 the. Tlie whole of the working instnimenUi, whkk 
arn io 11 certain extent olidolete, are un the liet to be reuuwed wb*a 
tlif time can be devf^ted tn them. 

The equatorial has not been in regular commissioa during lit 
yi^ar, as some adjnatment.s re()aire to be made. 

The seismc{j[raph, which had been diamiintled owing to the 
efiectfl of tliti heavy blasting operations by the Sydney Harbom 
Trust, was not a^nin put into conimissicin till May 1 7. The reooid 
of the San Franciaco earthquake of April iS was therefore lo«L 

The buildings of the observfttory havK been ronovatud throng^ 
out and two new rooms added. Thit« will cverc-onie the congutioo 
in some of the offices CAiiflt?d by the acnnmulation of many yean 
meteorological records, which, under the old eonditioos, for waul 
of a]ia<'-e, bad to bo stncked on the Boors of the rnoma. 

With regard to the future of the obaervatory, the Comoxv 
woitllh Oovernment has decided to deal with meteorology only, 
leaving the astronomicnl wi>rk with the Slate Government. Tb< 
future arrangements for its control are still uncertain, and it i> nol 
yet decided whether the observatory will remain in the nui 
building or be sent to the clearer atmosphere of Pennant HilU. 
where the astrographic work h at pri'scnt carried on. 

The astrtmomicnl asHiatants, Messrs Knymond and MertialdL 
have observed during the year with the transit circlf*. and titt 
reaultB are as under: — 



Number of R.A. observations of stara . 

N.P.D. .. . . 

„ K.A. „ of Sitn . 

— making a tntal of R.A. observations . 



. 3495 
2IZ4 

• 455 

• 3950 

The 9 A.M. collimation, level, and nndir observations 30S of 1 
The 9 P.M. level and nadir obserrntions 147 

AximutliK determined from 137 pairs of circuupolar atan. 



^Teb. 1907. Eigkiy-seventk Annual General Meeting, 267 

Tfafi year 1906 hai) been particalarly favouniblo for DbBervatioiu, 
\% gruatur DUtnbor of stars having been observed than for a good 
[SDaDj years past. The greater bulk of t)io observations Kcre made 
jduring the winter monthK, wh^n the definition was Iir»t-cla88. The 
^3905 Catalogue has been prepared, checked by the junior com- 
[puters, and only the ubatract remainH to be made Ui Bnaljy cum- 
[pletfi it. In addition, thu KA.'h and N.P.D.'k of nearly all tlie 
<obEer\-atioi)S made during 1906 have been checked, and the 1906 
[Catuloguo will be put in band at ooce. 

1605 visitors have registered their nainee during the year. 
[Of this number, 710 attended the evening lectures with the 
]ualorial and tanlem. 
Tbo astri'graphic work at the Red Hill brunch has boon carried 
on by autronomical photographer Mr J. W. Short, who, in addition, 
haa chai^o of the niogmitir, work. The magnetic instrument, an 
old ouc, has been compared with the modem instrument at the 
Molbourne Oheervatory, and, owing to the report received, it baa 
been derided to get a set of new magnet«. The Director of llio 
Kow (England) Observatory has l)een asked to obtain these, and to 
ci'rtify to the errurtt, etc. before be accepts them. It is hoped that 
they will b« ryceivt-d by April next. 

Owing to the instrument being away part of the year in 
^Melbourne the magnetic ohftervations were Incomplete, but the 
declination and dip remain practically constant. 

Plates expoaed. — Catalogue plates, 31 ; chart plates, 157. 
Total number of plates useid, 175. 

Photographs were al><o taken of the oocultatioD of Saturn iu 
October. 

Many of the plutoM taken have lieen sank to Melbonme to be 
measured by tlie Joint Meat^uring Bureau (Sydney and Melbourne). 
The number of tine nigbta wm 115, partially fine lao, and the 
remainder cloudy -tiid wet. 

Lifn-anj. — Mr (Iraham reports that the library received, by 
way of exchange from other observatories and institutions, 1050 
books, |>ttmphlctA, and papera, being an increase ovar that of 
1905 by 5 per cent. 

The publications diatribuU^d were very few — only zoo. This 
is due to the discontinuance of the publisliing of the annual rain 
and meteorological roports. The distributions w" -••t' un- 

favourably with thoMf of the year 19051 were 

sent out. 

The library is being gradually • 
catalogue formed. 



(ibserTBtions were mad" t'l 
February. During the great 
in England, and advaiilag? # 




268 Report of the Council to the Lxvn. 4, 

the observations made since 1891 reduced. This work, which ii 
now nearly completed, was facilitated by a grant from the Sooth 
African Association for the Advancement of Science, to whom, u 
well as to Sir David Qill, the Director wishes to express t^ 
acknowledgments. 

Mr Tebbutt's Observatory, Windsor, New South Wtdea. 

For the reasons stated in the Annual Report of the Observatofy 
for 1903, regular observations were discontinued at the close of 
that year. There is, therefore, little to record for the year 1906. 
The only astronomical observations made were some measures of 
the well-known binary p Eridani and observations of the lanar 
occultation of Saturn and Titan on 1906 October 27. These 
observations have all been sent to the Society for publicaticm. 
The usual meteorological observations were also taken. 



^p'eb. 1907. Eighty-seventh Annual General Meeting. 


269 H 


^K KOTKS ON WME PoiNTS CONNBOTID WITH THB 


pROUKBSa 


I 


^L or Astronomy dorino thb Past Year. 


^^1 


^V Discovery of Minor Pianet$ in 1906. 




^H 


^B One bundrol and fiovCDteeii aew plaueto vrure 


discovem 


^^^^B 


^1 first annoiiMved in 1906, as follows; — 




^^B 


I P| || 1 


n n 1 


hi 




^1 


H SJ ... Jan. 15 E 


HT»... Mm. 5(o2)W 


us .. 


Aug. 22 


H 


B»L ... za W 


3D' ... Notr. 3(05)Ly 


UT ... 


22 


1 


Bsu ... 22 W 


Tf S9> Mar. 14 K 


UU ... 


27 


1 


HaN ... 32 W 


Tlj ... [7 W 


trv ... 


28 


H 


B 80 $83 33 K 


TR ... 17 W 


ux .. 


Sept. 12 


1 


W 8K ... 2A W 


TS 592 [8 W 


UY ... 


12 


1 


SS ... 24 W 


TT 593 30 K 


VA ... 


17 


1 


ST ... 24 W 


TU ... 30 W 


VB ... 


18 


1 


SU ... 24 W 


TV ... 21 W 


vc . 


18 


1 


av ... 34 w 


TW 594 37 W 


VD ... 


iS 


1 


3W ... 24 W 


TX ... 27 W 


VK .,. 


•S 


H 


3Y 584 IS K 


TY ... 37 W 


VF ... 


24 


^1 


aZ . . Feb. 16 W 


TY» ... Mar. 27 W 


VG . 


24 


1 


TA S«5 16 K 


TZ 595 2? W 


VH ... 


u 


1 


TB .. 16 W 


UA 596 Feb. 21 W 


VJ ... 


36 


1 


TC 5S6 21 W 


00* Ang. 12 (04) 


VK ... 


2ti 


1 


TD ... 21 W 


UB 597 A[)r. 16 W 


VL ... 


"4 


1 


TB ... 16 M 


UC 598 13 w 


VII ... 


24 


fl 


T? 587 32 W 


U.] 599 25 M 


VN ... 


OcU 8 


fl 


TG 588 22 W 


UK ... Mar 13 W 


vo ... 


8 


fl 


TH ... 23 W 


UL ... 29 W 


VP ... 


II 


^1 


TJ ... t6 M 


UM 600 June M ^1 


vg 


11 


H 


TK ... 16 M 


UN 601 21 W 


VE .. 


II 


^1 


TL ... 33 M 


no . July 30 W 


V8 ... 


II 


^1 


TM 5S9 M&r. 3 K 


UP Aug. 13 K 


VT 


8 


^1 


TN . 3 W 


L"Q .. 22 W 


VU 


17 


^1 


■ to 59a 4 W 


UK ... 33 W 


vv 


n 


^j 



270 



BepoH of the Council to the 



Lsva 






WF .,. Not. 9 
WO ... 9 

WH... II 






t 



111 






WJ . . Nov. u 



K WW... Dao. » 



\VK... 
WL ... 
WM... 
WN... 
WO.. 

wp... 

WK ... 

\V8 ... 
WT ... 
WU ... 

v/v ... 



II 
II 

10 

u 

12 

u 

■4 

'4 

<9 

Dm. 7 

7 



K I WX 
K WY 
WZ 
Xk 
XB 

xc 

XD 

XK 



& 
L 
M 

H 
H 

M 

M |XF 

M XH 



at 

X3 
2i 
3t 
3t 

ai 

«3 

18 
18 
18 
iS 



The year of dificover)" ia 1906 unlpaa otherwiae noMd ; Ihf 
ahbreviatiouB {02) (04) (05) stanii for 1902, 1904, X905. Tbt 
iiiitiaU represuut G, Gotz; K, Kopff; Ly, Loowy ; L, lilinert. 
M, Metcalf ; W, Wulf. All the discoveries were made at Heidel- 
berg, except thoao by M. I^ewy (at Paris) and Dr AleU-alf ; Uw 
lAtter gentleman'a oba>-rvati>ry is at Taunton, Mass., U.S.A.1 aW 
be has adopted the methi^d of guiding the telescope so as to mort 
at the rate of ao average minor planet moving psrallel to ibt 
ecliptic. In this way fointer planet£ can be photographed, aiDoe 
their traiU are much shorter. Planeta ure distinguisbeJ ^om 
photographic defects by two exjiosureH, with a shift in declioaticc 
between them. 

The foUowiog planets not numbered at the dat« of tb« tut 
rep'irt have since received permanent numbers ; Q£ 570, QZ 571. 
KB 572, RC 573, RL) 574, KE 575, RF 576, RH 577, RZ 578, 
SD 579. SK 580, SH 5S1, SP 583. 

The following errata in the last report (vol. Ixvi. p. 217) ouj 
be pointed out : — RT, not RN, is identical with 477 IlaUa ; HB, not 
HA, ia identical with 526 Jena; for Oello, ttenna, recbJOcllo, G«naL 
The followinjj planets do not receive permanent numbers, not 
having been aufficiently obBerved : — RG, RJ, RL, RM, RK, 
RP. RQ, RR, RS, RU, RV, RW, RX. RY. SA, SB. SC, S 
SG, Sd, SL, SM, SN, SR, SS. ST, SU, SV, SW. SZ, TB, 
TE, TH, Tl, TK, TL, TN, TQ, TR, TU, TV, T.\, TV. TY», UK, 
UL, UO, TIP, IJQ, UR. US. 

The following identities have Iwen eutabliahed : — CR (poaaibtj) 
488, CX 554, KR = KV, KY 529. SF 488, SK 275, SQ 411. 
SX 88, UD 181, UK 410, UF 394, UG 149. UH 431. XTW 6t, 
VZ 408, WQ 167, 469 <» 488 ; the number 469 has been trauaferrti! 
to GE (diacovered 1901). 

The foUowing pWneUi ^se \MeTv VMim«d-. — 400 Durrota, 459 



, not 

M 

run 



Feb. 1907. Eiffhiy-seventh Annual General Meeting. 271 



I 



hS^^, 461 Saskia, 463 LoUit 464 Megaira^ 465 Aletio, 466 
'~~ ipAoR«, 467 Lavrat 46S Lino, 469 Arffentina, 471 Payxipeno, 
473 A'o/Ii, 474 /Vwrfmiwi, 479 C'lprtra, 480 Hansa, 481 Kmita, 
490 FeWia*, 492 Oietnonda, 495 FAdalia, 500 .S<r/tiri«r, 501 
VrhixiduT, 502 Sigune^ 513 CVntortmo, 514 vfrnib/ti, 515 .^tAa/ia, 
524 fideii*, 525 Adelaide, 536 t/«na, 527 Enryanthe, 528 Hetia, 
529 PrecioM, 530 Turandal, 531 ^;T/tVia, 536 Aterapt, 538 
Pnederike, 539 Pamiwi, 540 Jtoeamuade, 541 DeboraJi, 543 
Charlotte, 545 M&fmiina, 546 Hrrodiat, 547 Fraaredis, 548 
Krewida, 549 Je»»"nda, 550 S^a, 551 Ortritd, 552 Siffeiindf, 
553 Kundry, 555 -Vorma. 556 /'ft/zHw, 557 Violetta, 558 Carmen. 
559 A'anoM, 560 Delita, 561 hvjvcelde, 562 Salome, 563 Suteika, 
564 i>B(/w, 567 Meutheria, 58 1 Tauntottia. 

The iiiUrr&Htiiig pl(tii<;U 2'huls nitd yjrb'/mniar^ were photo- 
graphed at Heidelberg, aLxo 294 Felu-ia, whtoh had not Imcd aeen 
since 1891. 

It ii! hardly iieceaMiry to wy that 1906 bivaks all records for 
tbir number of discoveries; it has, indeed, prarticatlj doubled the 
previous record of 59 in j 904. It is, of coui-se, likely thai a i*rtain 
mimVier of the planetB descril-eil as new will be Riibsequently found 
to be old ontifl r^obHcrved, but in any cHtto the numbur of uctnul 
discovtriea niu«t l>e very lar^e, showlut" that the hopes expreiised a 
few years Jtgo that the zone was npproacbiDv; exhauritton were 
decidedly premature. As if to show that the search for planet* 
cannot be almndoneJ without the risk of losing some very interest- 
ing objects, one of the bodies discovertnl hist year has a very 
remarkable orbit. This i» TG 588, which Dr Berberich baa found 
to liQve a mean di^tnnco almost (perhapa eitnctly) the aame as that 
of Jupiter, and a lar^e eccentricity, so that its aphelion distance is 
6*2, nn entire a.stroiiuinical unit beyond /u/ji/t'ji mean iliulance. 
The planet's heliocentric longitude al discovery was 55^° greater 
than that of Jufiter, ftvm which Dr Churlier concludes that it is 
■very prol»ablo that the Sun, Jupiter, and 588 illustnite Lagrange's 
proposition that throe ma^es at the anglet* of nn ef|nilaterai triangle 
wil^ if properly projecte'J, cooliuue to move with unchangeil 
relative coutigumtiun abunt their common centre of gravity. 
Since the orbits of both Jupiter and 5S8 are ecnvntrii', and their 
planes inclined to each other at an angle of about to', the above 
conditions are not rigorously fulGUed ; but provid&it certain hmita 

uot exceeded, they could oscillate about the eijuiluteral pmilion 

a mean. The re-nbservation of 5S8 may b« expected sbortJv 
when it will presuiunhly lie possible t4i ascertain w!)eth**r it«i 
motion is the same as that of Jupiier, in which case Dr C 
hypothesis is ptotiably correct. Dr BerN-rich's element" 
are given. £]»och 1906, Feb. 22*5, Berlin M.T., M df 
w i2o" 35' 50°, a 315" 34' 7", i lo' 20* 53", ^ 

/* »95"'>3. loK« o'7'999- 

The Berliner Jaltrhufh for 1908 gives \ 
about the oh&ervation ol the muior planettt 1 
1906: — 388 planets bud Imicu observed at 



- plai 

I 



273 



Report qffhc Council to the 



LXTtL4. 



31 at 3 op|MMitioiiB, 53 at 3 oppositioiu, 97 at i opposilion only. 
It is of interest to ^wk thu Hctual Utit of these lost planot« inm 
I to 400 iudueive:— 99, 132, 155, 193, aao, 285. 290, 293,399, 

3>o. 3i5. 3i6t 3«. 3^3. 33o, 353. 357. 36^. 39». 396, 398, 400. 

A. a D. ** 



The New Sal^IUeg of Jupittr ami tyntum 

Ptiring tlie past ye&r br F. £. Kjwu has published the foUov- 
inf! r«vined elements of Jupiler VII., roEerred to the Bartfa^ 
equator. 

£p<)di. 1906 Jmi. om 0. M.T. 

P= iS*-? «=o-zo8 

■■=115* »-i"-386 

a^aqi* 1oi<. {i = 8'S946 

<= 25' 28' Peril") 359*7 

Recent Greenwich observatioiis wem to sbov that the sbon 
perioil ia ecinienhiit too long ; probably tb« value 357 day* is ueam 
the truth. 

A Buccftisrul search has been ma<le on the Barvanl plates tot 
images of Jupiier VT. lu the years preceding its discover)' {Harvard 
Anaala, voL Ix. No. 11). The following positions are given : — 

d 
1894 JftQ- 25-563 G.M.T. 
1S99 June 26*561 „ 

.. .. 37*588 „ 

„ „ 30*566 „ 

„ July 1*594 .. 

„ „ I2TS05 „ 

A position ^veu for 1S94 Ftbrnary 2 is omitted hero, since it it 
ioeoneistent with that for .lanuary 25, and the i<)entity of the obj 
ohaerved witli the mitellite iteeina doubtful. The chid value of 
above poeitioDS will be tu improve the value of the sidere&l period,] 
and possibly also Ute suculnr chunjiios in the elements. For t his pt 
pose it will be necp-^tary to comptite the pert url«t ions for the ut 
dates. However, iht^r (effect divided by so many revolutions etumt 
he8erir>u4, and the values of the period obtained by neglecting tl 
are probably near the truth : these arc 35o'^'3 from the 1894 poailti« 
250"'5 from the as»Gmbla<,'0 of the 1 899 ones : as tlm recent observi 
tions appear to imlioate 25o'*'7, it is probable Ihnt the taIe 
35o'*-5 is within o""-! of th.- truth. The periods of VI., VII. are 
nearly equ^l that uoiiie thirty years are required for VI. to gun » 
revolution on Vli. 

Profeuor Pickering notes in the same number of the Am/tait 



R.A. 


Dm. 


-33075 
+ 2 54*42 


+ 2*51'^ 
*-6 i6'3 


f 2 56-01 


+ 6 07 


+ 359-30 


+ 5»o-3 


+ 3 0'20 


+ 5 7*4 


+ 356-38 


+ 2 77 



J 



Febi 1907. Fiffhty-atvmih Annual Gtntral Meding. 273 



dut " tb« tenth BateUita of Settum, which is an tsxceedingly difficult 
object, can be seen wheu within 2 of the planet." 

Aitr. Nftehr. No. 3143 contains an ephcnieris of •/apiter Vl. 
calculated by J. K Martin, of Washington, from unpublished 
elements by Dr F. E, Boas, extending from 1906 Aogost ao to 
1907 April 17. The discordances between prediction and obmrra- 
tioD are small, as is also the case with Dr Ross' cphemeria of 
Pheebe, of which numerous obeerraLioua have been obtained at 
Arequipa daring 1906. 

The following table gives a Bummary of the Phoebe obaerva- 
twoB : — 

NHialwrof 
NIcbto. 

A. C. D. 0. 



Date. 


Vfb^ 


-Tkb.R.A. 


OtN«. 


-I^b-Dnc 


1906 Uay 19*4 




• 




0'3 


JuDF 37 '4 




-0^ 




0*0 


Aui;. 16x1 




-0-8 




-0'3 


.. «3-S 




-0*9 




CD 


&>pt 14*6 




-1-6 




-O'l 



TAe Cotnets of 1906. 

The number of comets discovered and obeei'vod during the 
past year baa been unuAually large. Some of th^ particulars 
connected with their history can be must conveniently exhibited 
io a table. 



<*iimat*« IVtlirTiiition 



Gaiiipt 1905 b 



19050 

190611 
19066 

1906 « 

1906 d (FinU)) 

1906 « 

1906/ (Holmes) 
I* 




« 



July 
Aug. 



17 
16 
22 

38 



Sdmsr. 

Giocobini. 

Brot>ka 

Koptf. 

KoplT. 

Hax Wolt 

Tliisle. 

Mctwir. 



H 
1906. 

Jau. 



Mar. 

Apr. 
May. 

Apr. 
Still rinibttf. 

Oct. 
Still vbible. 



?2, 

as 

^1^ 



Oot. 35 

1906. 

Jnn. 33 

1905- 

IW. 33 

Oct. 
I' 

V 



111 
I9OS. 

V. 
1906. 

I. 
1905. 




274 licport of the Council to tfu LXTU. 4- 

NeoeasarUy, the orbits are not yet definitive, so ibAt tU 
ciilalogQed order truunot be regarUcd as finally t%itled. Sab*fr 
quent diacoveriefi may further disturb the designattoD. But tbe 
divergencfle f rom the order of discovery are itafBciently rcnurkahb, 
and must Dot be overlouketl. 

The tint two eoniets od the list wero mentioned in the last 
Annual Report. Comet 1905 V. calls for no furtiier nanaik. 
Afi anticipated, ooiuet 1906 L was observed al tlio Cape of 
(tood Llope, Atid subseqaontl; at other observaturios in Europi 
and Ainericu. 

Cuinet 1905 VI. ia of the ordinary parabolic elaaa, and 
possesses no puliite of iiiterfHC. 

Comet 1905 IV. wii6 actually photographed at the KoDtpriuW 
Observatory on 1905 January 14, or 413 dayn earlier tluB 
Dr KupfTs aanouiiicement. The orbit is remarkable for tfaf 
lat>^ Perihelion <li)ttaiieu (3-3 K). This duttauce has been ex- 
ceeded only in the case of the ctomet of 1729. The nioti»n mat 
be re^jarded aa parabolic, thmigli an elliptte of 1153 years' peh<xf 
has resulted from compulations in which no assumption jvras luadt 
rcjiarding thw excentri^ity. 

Comet 1 906 I J. was discovered in the soulbem hemispben, 
and was very unfortunately situated for Kuroiwan ob«ervutorit». 
The obeervationa, few in number, extend over little more liian 
three weeks. The uleinentH, though un<:ertaiu, appear tu be of 
the ordinary parabolic claiw. TUi^ ih the more probable oTing 
the large iDcIinatiou, the moiioo being uearly pcrpoudicuhu* to 
le ecliptic. 

Comet 1906 V. is the third retnru of the comet of Finis}', 
which pautied utidottictvd iu 1S99-1900. The accumulated e: 
in thi; meaiL anomaly in this luu^' interval, ariaing from ne^' 
of porturltatiuiis and other i-auHee, made the ephemeris calcula 
by M. Fayot, from the elements of M. Scbulhnf, somewhat 
certain. The jiOHition wilh regard to our horizon is nut tmj 
favourable for observatiun, but the opportunity these ohserratiotu 
afford for correcting the mean motion is most fortunate, since, ia 
tlio next rt'volutiun, the comet will apjjruucli {in lylo) so el«e 
to Jujiitfn' as to ."(uffor very conxideraMe perturbations. Obs^m- 
tioiiR at the next return will afford very exact means for de 
mining the itia.si? of that planet. 

Cornet 1906 IV. proved to be one of the family of ahoi 
{leriod cometn. The ohspiTatioiis did not brgin till after the 
perihelion passage, and could not be pursued very long; but 
the elliptic character is well marked. 

Comet 1906 TIL is the secmd return of Holmes* Comet. A 
very few observalioni^, and only with the large eqaatoriala of the 
lick and Yerkes Ohservntorips, were obtained in 1899—1900, 
but r>r Zwiers found these sufficient to correct the ebnaenu, 
and, after allowing' for the etfect of {wrturbation by JupUer, h* 
was able to supply an ephemeris which repre»ent4-d the patJb ol 
the ctimel wilh great ivccuttlc^. From, this ephemeriB Dr Ml 



,Uy, 



01^^ 



1 



iFeb. 1907. EigfUy-tevtittk Annual General Meeting. 27$ 

Wolf aticceeded in photographing the comet on August 28, and 
though the object wati, uud luu remained, vury faint, it is prubiibly 
Btill uudor observation in the largest ttitescujies. 

Comet 1906 VII. iit a tolembly hrij^lit comet, Htill visible, 
who&e motion can be repreaented by a parabola. 

Comet 1906 VI. is a faint object, (UscovtTcd on a iihotofrraphjc 
plate by Mr Metcalf. of Tauiitnn, U.S.A. Tbe observations hsTe 
[jiot been very uumeroua, and, like some others mentioned, have 
all been pi^it-periliolioii, but theru it; no doubt the ubjor.t belongs 
to the family of short-period comets. The most probiible period 
IB nbimt 7^ yuan ; and the cleiiienbi bear a vet}' strong raaemblance 
to those of Faye, Wolf, and some others. 

The orbiia of the following comots have been detinitively 
determined during the year ; — , 



I 



I 



Oonwt 
IJ43\. 
181911. 
1826 T. 
1844 III. 
1864 HI. 

1874 n. 

1883 I. 



Oluntcurol 

vr1>U. 

KlUptic 

rnr»bolic{l) 

Blliptb 

£]tipLic 

Ptrsbulic 

Hyperbolic 



CilcuiBior- 


ARthofity. 


B. Culm 


AM. NfifA. Vv. 4111, 


Peck 


AH. Jinimai, Nos. 584-5 


Bnat«)c 


Sfntaeh. tyitn AJc, 77 


Payt't 


Thimm, FariM, 1906 


SohrooUr 


Oa. li. Win. CkruL 1905 


Biirgxraf 


Siizh. Wien Ak. 1904 


H«llebiaDil 


An. AVA. Ko, 4090 



The reituit of the calculation in the case of 1826 V. ia not 
very satisfactory, since .some of the outstanding residuals ara 
large. 1844 TTL, according to E^>nd'9 calculations {A^. J&urtuxU 
103), gave marked evidence of hyperbolic motion. Fayet's new 
reduction of the observations does not conBrm this suggestion. 
In the coeo uf 1883 I. a parabola would amply satisfy the 
observations ; the hyperbola ia a oomptttational result. 



w. B. p. 



Progngt 0/ JHeteorie Aitlnmtnny in 1906. 



H Meteoric obfti>rvation doos not appear to have made aul 
I progress in 1906. Obxerrers were few. and no •p.;cifillj 

■ showers attracted attention. The PstiteuU rettirniid at n 

■ of very unaettled wva^Uer, and the LeonHa and An-tr 
I failed to present active a|if»earAricw. 

The Biiot.ui« (or Qu^idrantids) ■'■ ■ 
of January 3, faniishing some bn ,1:. 
the display cuuld not be closely watcbed •' 
gathered over the sky. 

The Lyrid* were wt-U obe4)rTeil I . 



.«tl( 



'.kktifc! 




276 Report o/the CQundl to the 

near Hudilt<nifieM, on April 21. In 3^ 40™, between 
14'', bo couDied 37 [ticttfors, including about 30 LyridM, ftvm • 
rndiiint aj.pnrentiv double at 267^' +35° to 275'' +•31'". Thn toeiB 
jKJsition at 371 4-33' agrees exactly with the best prenrjou 
■letenuiimtionH uf the rilitin-er-centro. 'Vhe Li/ruh aeen hy Mr 
Bruok W4;re quick, and h proporttuQ of tbcui left straaki. Ctn 
April 20, during nearly ati hour, only one meteor was recortlal, 
90 (liiit tbe nifiximuni np|)»irH unduu)>tedly to bare occturad at 
April 2 1, and to have fiiniislied eome similar cboracteristia W 
the diKplay or 1901 April 3t. 

The Augrust Pertt^A^ig returned in about average strength, boi 
partial uiuonligbt nuU stormy weather prevented much obeuvatian 
until Au^ntst 12, 13, and 14, when a fair number of met«an wen 
seen hj Miiw Irene Warner, of Horfield, Bristol, as folluwa: — 

Aug. 10, 9p to ii\ 15 meteor*. Many clowk 

„ 13. II to 12, 16 nieleors. Partly dear. 

' ,1 13. 30 meteurA per ^ouT. 2/3"** /Waeiffa. Cleared aftir 

storms. 
„ 14. 20 meteors per hour. 1/3^ P^mtids. Cleared afw 



storma. 



i 



On Octobfcr 22, lo"" 15™ to 13'' 25"", Mr C. L. Hrook saw 36 
mcttiont, incluiliiig several Orumidn. At i a** 1 6^" a third oiog. meteor 
was doubly observed by Mr Brook and by Mr J. P. Kenyoa tX 
StixUciioit from a ru'ilant at 98° + i-f". Tliis wait an example of ilu 
( Oeminitl*, and the latter system at the Ocioljer epocfa appean 
to hare furnished a richer display than thp (}rioni*ttt in receal 
years. 

About the middle of November a few of the usual fitrenkio; 
Lsohuh were remarked, and several brilliant fireballs, including 
LeoniiU and J\inrirh, wyre ]Bportvd. Ou November 16, at 13^ 20", 
what appears W havf* heen a mui^iKcent L«/»tul wag seen it 
HampHteitd, N.W., and Waltsjo-on-Thamea. It gave a fla^b UkflJ 
lightning and left a streak for ^verul minutes, but the obeervation^B 
are not sulGcifntly aceurnte or numerous to aSbrd uaeful dednctionj 
as ti ihe reft] path. On the evening of Novomber 17, belweea. 
1 1** 9*" and 1 1*' 40", Mr Hrook registered three dote-nurvfng Levnv 
One of these was also noted by Mr Eeuyoo, and it had a velocttf' 
certainly not exceeding 30 miles per second. It is trpquon 
found that the swifter class of meteors during borizoutal Higbu 
exhibit unduly mlow motioUi a» though encountering great atmo- 
spheric rrixistance. As another case of the same kind, the veiy^| 
loDg-pathed Aquarid observed by Professor Herschel and Mr^l 
Bridgvr on 1900 May 3 may bu mentioned; this object bad ■ 
visible fliL^ht uf 155 miles and a veU>city of 28 miles per aecood, 
which is much less than the tbeorutical speed of about 40 milat 
Iter second. 

"Hie Ijfvmid* were weW obsftTNtA Vj "NVt C V. OUvier, at tfae 



resfl. ^ 
ntlff 



^etai 1907. £igit^ M trtntk AiunuU Otntrml Mating. 



^77 



VeConniek Obsemitury, UniTsnity of YiiK>&u, U.6^, 
SKotcmbcr 16, and Uie following nnmben wer<i cuutited : 



Um^ta. 



tltban. 



ToisL 



10 u 




7 


s 


n«u-. Uo JiMt rUj 


■3 O-IJ 




ID 


14 




\\ 0-14 




8 


<7 




M o>i4 II 




1 


4 




M :^is 




3 


6 




15 e-16 


M 


13 


J« 




16 0-17 


14 


10 


i4 


Cloiid» nMr horiioii. 


17 0-17 21 




3 


6 


P4rt cloudy. 



5» 



S3 



105 



Eight of the LeottifU «rere eqaul to first magni(ade stars. Tho 
, prerailiitij colour vaa yellow, but there were many graen and a few 
I red onea. The finest meteor Mr Olivier «ver obflerred came at 
17^ 5>*- It v*^ equal to the moon at 6rat t)uarU>r, anil t-O'let) al 
^ VirgimU aft«r n path of only 3°. From 1 1 nieteon* pUttted uear 
the radiant, tho centre uanie out at 151" -f 22*. Thu »treak» left 
by some of the meteore were very |>er8iBteiit, and the display was 
considered very good, coueidonng its lateanw. Sevenil minor 
radiaotd were in strong activity. These detiiils are KJven in 
Popniar Astrtmowtj for January 1907. 

Mr Brook nttnessed a fairly active return of the OtminiiU 
on December is (« few were also noticed on Dep*r»ber 13), 
and bright meteors were seen on Iiecember 12, 13'* 35°*, and 
December 15, 6'' 40'". On Dec. 12, during watuliea iimoUiitiug 
to 2'' 42'", between lo** 35*" and 13*" 43", 51 moteom weni set-n 
(of which 26 were rfgieitereil), and many othere mui>t have escjipud 
observation. 

A counderabli- number of fireballs and Xar^n metoora of various 
Icinds bare been reported during the year, but, excoi>t in n few 
inatancefi, the descriptions were not so precise and coruplete that 
tbc real patha might be derived. It ia to be bo|HMl that mon* 
attentioD will be giveo to thiR partioular brunch of oljecrvaiion, and 
every effort made to secure the ncietwary data for aecerlaiiiiug the 
heights, velocities, and radiants of these tnt«roating bodi^. The* 
UiUally make their apparitiuoH at times when least exiiecttMJ, p 
are ufU-'D ueca accidentally, but their poniliunu and direcl 
amongst the etartt should always be registeretl with the tt< 
accuracy poseible under the el rcu instances. 

Ill 1906 the following real patha were oompotod for is 
seen in this country :- — 



278 



Rsport of tlu Cowneil tu the 



LXVn.4, 



DwU. 

1406 


a.iLT. 

h n 
83J 


Brlvht* 
am*. 


H«iKlit 
■triraL 

HtlM. 

59 


H<(Kbt 

itKnd. 

45 


HOaiu 
42 


Volodtj- 

MUm 

p«rK*e. 

24 


lUdlaat 
roUL 
■ 4 

31*4 + S3 




Feb. ij 


10 42 


9 


61 


2S 


36 




1051-st 


iV 


Mm. 33 


to 52 


i=» 


6S 


45 


47 




3184-10 




A]*ril IS 


S 6- 


it 9 


65 


z8 


39 


tS 


»53 + J3 




16 


853 


>]1 


69' 


aa 


SJ 


'S 


1S7 + 33 




31 


'3 4 


>9l>tlM 


89 


56 


33 


as 


»754-35 


J 


Aog. 5 


10 33 


>9 


65 


52 


24 


30 


384.5s 


S«pL 1 


10 


>I 


79 


40 


5» 




330^)3 


i ■ 


«s 


10 34 


3* » 


77 


43 


72 


31 


a4S + 3«» 


m 


a? 


6 59 


3-1) >9 


63 


45 


4£ 


I 


345+ ' 


iT 


Oct. 3a 


13 t6 


3-1 


75 


56 


44 


98 + 14 




KOT. 17 


11 9 


I 


77 


66 


9' 


y 


150+31 




n 


8 5 


> 9 


59 


36 


5* 


21 


46+ $ 





Jan. 37. A very hrilliknt object, sathfaetiirily obeorfttd. 

Mar. 23. Tbfi radiant poiot is uncertain. 

April 31. The radiant may have been ut 394" ±0' &nd hagltt 

of the meteor 87 to 79 miles. 
Aug. 5. A fine, flashing }Wmd, leaving 4 strvak visible fw 

20 sees, thiiugh tlie full moon was $liiniii^. 
Sept I. The radiant poasibly at 314'+ lo\ 
Nov. 17. A bright Levnid, with ubnormally slow motian. 



J^atl 0/ a MMmritt at Sea. — Capt. Andenmn of tho 
A/riran Prince, writing tu hia priiicipalH, .says, " We oometobif 
bear of veHsnlii diaappeariiig during a passage of fine weather lad 
in the open sea, free from navigation dangers. My exfwrientt » 
the voyage from New York bos BUggestsd to my mind that aiap 
may have occaeionoJIy betm lost by meteors falling on thunu 

"On the evening of Oct. 17, igo6, 1 was on the briilgt- with tbe 
second olHcer, when suddenly the dark night became oa light u 
day and an immense meteor shot perpendicularly towards the earth. 
Ita train of light was a broad etectrie coloured hautl, gmdoaDy 
turning tg orange, and then to the colour of molten metal. Hm 
meteor entered the water with a lusaing noise close Ut the aUp, 
and the cuuwquvnce, had it struck uur ship, would have hoc* 
annihilation." w. r. ol 

.S'ofar AlUiviiy in 1906. 

Sun-spots.— Ihti general character of the sun-afiot acti 
1906 has been that of the last pliaiie of maximum. Tbt 
been a distinct falling oflT in the mean daily spotted area 1 
pared with 1905, Ibuugh spot-groups have still beeii nm 
especially iu the Dorthern hemisphere. But the giaat gro 



I Feb. 1907. EiglUy-scv^Uh Annual General Meeihig. 279 
charactemtic uf 1905 have been much less frequent, mid the 
tendency h^ Wen raiher to dcvulop long processiuuit of groups of 

I moderate size following eauli other at short intervals along n 
parallel of latitude, titan to concentrates into f;nsat diatarbftnces. 
Still, gruups of the 6rat order oi niHgaiturle weru seen on four 
oci»8ioiis durtnit the yv.ar, viz. — January 21-30, March 16-27, 
July 27-AugUftt 5, ami December 12-25 — '*° great dialurbaacett 
beinK »n ihc ili^c at the Ninie time duriuff the last of th^&o periods. 
Tlicfu was 11 very striking set-'ondary niiuimuin iu October, the miii 
being free from spots on no fewer than nine days in that month; 
but a difttinct revival set in in Novembftr, and thu year clused with 
a period of ^reat aclivlly. The mean daily total aputt<xl area will 
probably work out as abuut Uirr^e-fourthK that for 1905, eo that the 
creat of the wave neems to have been passed ; it may provisionally 
be tukon aH boiug plactid in October 1905. Faculin, on thu otiier 
bam), have been about as nutneroufi ns in 1905, and have, in 
igeneral, showt-d nu givat flnutuutioii from month Lu moDtk. 

The mean latitnde of the spotti^d area continued to he about 
13^ from the equator; that is to aay, thtt zone usually occupied at 
maxinmni has already been passed. k. w. m. 

The l^fiMTietie^. — The daily frequency of prominences deduced 
'from Bpectroheliograins taken on 45 daya during the year 1906 
[' WEN pnicttcally the tunio as that deduced for thu preceding year 
from pbotoyraphs secured at the Solar Physics Olwervatory, South 
Kensington. The pictures were taken through the " K " line 
(calciuui) of the solar apeclrtini, and iho lower limit for height of 
proQiinenceti accepted was ao". The preponderance of activity iu 
both years was niauife«it«d in the nortlmrn htiniiaphere of the 8uu, 
, the figareti obtained being as follows :— 

1 90 J. 1906. 

Iforth liemUpberv 3-4 3^9 

SriOtli „ 3*0 3< 



Total dAily rroqnuBor 



6-5 



The decreaae in the daily frequency for the ituutbem hemiflpbere 



I 



u noticeable, though the increase in the northern in 
balances it. I'h.e most activo prominence zonivt 
latitutlea, and in belts atiout 30' bighnr, Many c« 
nencex wt*ri! registered, while 6*5 |)er cent, of thp 
the n'hole limb were within lo degree» of thu St? 
From 'lunu 61I1 to tho nth u Htrong, pvnoi* 
group nf prominences was nhnwn clustered root 
the Sun. On a negatiTa taken on thr rrth J 
broken Hame of bright calcium. . 
radiuily from tho photosphere, «. 
western limb in the sjKit latitnde of * 
rapidly di»flp|)eared, for on an 
forty mtooles afterwards no trac 



uiiter- 
•t spot 



28o 



Report of tfie Cowicil to ih* 



LXVa4, 



The prominence activity for t)ie first ftix months of 1906 vu 
given by the late Profeaeor Mascari from visiiat obserratiocwi •( 
Catania, the lower limit for tbuir LL-ight Ufing taken «« 30'. k 
moderate iu*;riua8B of activity is indicatetl for thift half-year over the 
lueau of the preceding year. The me^n daily frequencies are u 
follows : — 

1905 . . . 3-02 

1906 (Krat six months) 3*93. 

This increase ia somewhat greater than that indicAted by \ht 
South Kaiidir^gfon photogmphe, thonah the actual daily frcqneDct. 
aspven by the negatives, is much higher. 

Mr Evershed, in his Ust report to the Society, gave + 75* awi 
- 75° for the promiuence limits in 1905. A remarkable feature 
the distrilmtion in 1906 wew the prominence activity ia 
neighbourhood of tha solar poles. In ti)e^£b8crvutioiis of M 
promint-nctii within 10' of thn solar poIeOlW recorded in 
years jvist jirecedinj; the sfjot maximum of iS.'^t ^"^ since 
date tiioy are sliarply reatricteii to the year i^yV Their »\i 
complete absence in the remaining years ia striking^ w. J. & u 



Tif 



Doubie Siar9. 

The same classiBcation is adopted as in previous rc/?'^ 
ahhreTiationa are : — ^ 

M. N. : Monthly Notices B.A.S. 
A. J. : Astiimornical Journal. 
L. O. B. : Lick Ohtertatory BuUeliti. 

A. N. : Astronomuc}ie Nuchric/iten, 

B. A. A. : Journal of lir\ti$h AstronomkcU' Astociaf' 
A. S. P. : Publieatiom of Agronomical Soe. of Pacui 

Ob*frmtion$ — 

fifii). T. E. Kepin. M. N. Ixvi. 7. A catalo^fae of 42] 
double ^tars in the zone + 30" to + 40". 

FhyA Obtrervatort/, Greenwich, if. iV. livi. 8. T^IeaBui 
double stara made in the year 1905 with the 38-incb refractor. 

John Tdibutt. M. A*. Izvi. 9. Measures of 6 sonthi 
binaries. 

Reo. T. E. Unpin. M. N. Ixvii. 3. A otUlogne of 80 
double stars iu the zone + 29° to + 34'. ^^ 

Rev. ?'. E. Espin. M. N. Ixvii 3. Siflflkl.fip licr^u^ 
and 27 midcellanoous starw made in 1906^ 

J. Nanffle. B. A. A. xvii. i. Mooaiii 

H. E. Lau. A. N. 4078. A set of : 
luneous pairs and 68 Slruvc paita madu for .1/' 

(f. ran BienffroeeJc. A. S'. 4107-8. A &ii 
made vith the 12-inch refractor at ileidfltwi 
pairs and 1 85 Strove pa\Ta mada ab VVq wi^ 



Feb. 1907. JSightyseventk Annital Ge7U7'ai Meeting. 281 



^ H. E. Lau. A. A^. 41 11. A c-ontiiiuation of tbo previous 
mfH5un*K, conluiiijii;^ 52 Sli-iive and z8 luiacvlliiuvDiiB pitirs. 

Ji. K. littnuird. A. N. 4128 A fine set of meHsurc« nf 61 
Cyjni on 144 ni;jlit8 (laat 1906 July 7, izj'-S^ az'-ja). Thfw do 
not confinu J>r Witstng's bypotbeais of a periodic oscillation in 
dliiCance. 

tE. E. iiamani. A. N. 4128, Measures of S 2398, S iiio, 
anil % 32Z0. 
W. Dvberek. A. N. 4130. A fine set of measurea of 200 
paire made at Houg-Koug io 1904-5. 
//. E. Lau. 'A. N. 4x34. Measures of f Ursa Majorts od 61 
nights in 1005-^. 

R. O. AHken. L. 0. B. 93. Catalogue of 350 new lioubles, 
of which 267 are separated les« than 2°. Tliis rual:&« 1250 of this 
cla-ss of double star discovered by Professor Aitken at Lick. 

H. Morgan. A. J. 584-5, MeaanTir^s of 19 double «tar« with 
the 1 3-inch MorriaoD icfractor. 
K R. G. Aitkin. A. S. P. 108. Muasure-s uf Hu 1176, A 570, 
y A 691, and discovery of S 2348 as a closu double. 

Calculatum — 

If*. Bowtjer and H. Funier. ^f. N. Uvi, 7. On the orbit and 
jiative ma**si'8 i*f 85 Pe'jasi (^ 733). Kaint star four times the 
of the bright star. 
A. C. D. Qrommdin. M. .V. livii, 2. Proper molion of 
Joitor. 

T. Lewie. Memoirs R.A.S. vol. Ivi. Measures of the stars 
)f Strove '» MenturtK Micrometrirn- collected and discu.it«ed. 
G. U. Hird. it. A. A. xv\i. 1. Note on a. Centauri, 
F. W. Dyron. B. A. A. ivii. i. Baview of Mernmrs R.A.S., 
Lvi. Struve double stars. 

A. C. I). Crommelin. President's Address. B. A. A. xv\\. i. 
Expttsitiun of Merrnfire R.A.ti., lvi. 

W. Uolterck, A. N. 41 10. Eli^ments of orbit of 85 Pegcm. 

I ir. DoherrJc. A. N. 4115. Kl«mant« of orbit of 70 Ophinchi. 

H. D. Curtis. L. 0. B. 98. The system of Castor. Kadial 

velocity curves showing both a^ and «^ to be sjiectiuscoi'ic 

binaries — a' the fainter^ 3'7 mag., has period 2*928 days ; 0"-, ma^. 

a'7, has period 9-2 19 day», 

B, G. AUketi. L. 0. B. 101. Orbit of j3 612 (period 34 + 
jaars). 

A. Hail. j4. J. 583. Note on /*W/c;rKiM. 

R. G. Aitkeit. A. iS. P. 104. Xote on 13 Ceti (period 7-1 



r^ 



A. S. P. 106. Note 00 95 Ceti, S 554, 971, 
Review of Mewoir* R.A.S. 



R. G. Aiiktn. 
and p 163. 

R. G. AUteti. A. S. P. no. 
Klvi. Struve double stats. 
" K \V. Maunder. A'liwc/f/yw, 1906 September, 
catalogue of double stars (review). 



A. ^tfsftX. 




382 



Riport of the Courteil to the 



Ob$erratory Xo. 369. Koto oa spactnl 




LXTIL 



Mi»*A.M, Clm-ke. 
ohautJ:cii o( { Booti». 

T. Letpi't. Observatory No. 373. Coloiire an<l magnitudes «Cj 
double kUlts. 

\V. J. HuMKy. Olnert'otory No. 376. A roeaioir oa iloal 
stars (review). 

R. T. A. Inne». Otmerraiory No. 379. Nolo on m Touenni. 

S. li'. HunUiam. Popuhr Aeiitmomy,xiv.^, 1906, Novemtccj 
ReTiew of li.A^S. Memoir, Ivi. t. u 



Variafiie Stars. 

FtogK$a iu the diMovery of new variable HtArs hna continual 
during' 190G, the bighe«t provixiona] namber allotted en fur to « 
new distiovery being 1906, 122 (A. N. 4131), and this ntimUr 
may tie taken to represent, at thf iesst, the uoiuber of nevr sun 
found iu the year. 

Harvard ColIef;c oyiairratory in in the front rank iu ibia line of 
researcb. Tbe following annovincemeiibt, among othera. hare 
tieen iii»de : — 



n.c.o. 

Olrcalar. 
107 
III 



130 



Kuuiliur (ft 
New Vkrlahl««. 

13 

32 
I 

31 



lUniarka. 

i.11 very fiiut Chiefly in Oriim and C^yvu 

DUcovervd from llioirtieculUrsftectrk. Prui- 
(ii[HiUj ill y. ht'iui3i[th'>re. 

In Carina, One i» Algtti type. 

CD.M. -30* 16169. V&riea I mag. in t«s 
dayo. Alijol typn. 

All inS. btmisphoro. ind priociiutlyin 4Ky, 
Caitaurut, <-«'. Ouu »( them l< Alyt4 ijy-- 

N«arly all rniiit. 

121 ■ iVvra PV/onm. Variation < II -J lo 9-8, I 

131 36 Principally in Cariva mid C&tUAvnu. S<k 

pmbnMy Al^l ^Tl"^* 

^fr A. Stanley Willintoa continues hiri dtudies of i^artain knova 
variables {A. J.). 

In H.C.O. Cireuiar 116, Professor E. C. Pickering, wilb 
obaracteriAtic energy, proposeii tbnt an the nuniber of known vaii 
ables now amounts to over 3000, the time in n[>e for tbe oon- 
pilation of a [>. M. of vnriahli; stars, with the view of asoertairtii-^- 
the prnportioii of tbi^ diffuniul- clasde*, and tbuirKeueral diatnbuti' 1 
in the lii^tivenfl. lie nKtiroatr-i^ thn number ot Ibc »lars uf ibr 
i6th inagitude and bri^httir nt fifty millions. JUa project involr» 
the fxamination of all Uie^o stum by thn method of superposin;; 
one pholo(;rapliic plat<' un nnothcr taLccu at a cHfTerent time from 
tbe 5r8t. It in, of course, a huge task, but with Ibo rapid and 
sweeping metbod indiviited it m considered as not beyond ih* 
powers of tbe preBent fienuration of obeerven. He oonsidere thai 



Fob. 1907. £ighlif -seventh Annual General Meeting. 283 

although ca-operatiott of a-slroaomera is necessary, there is itt {ireseot 
no need for a formal urgtHnisation and allotmenl of work. The 
iieM is so large as to admit of difterent ohservara working inde- 
peuduutly ; it is otity nNjuired that their work should not uvorlap 
or clash- 

Or A, W. ftobdrtH lias puhlifthed an important paper on "A 
>tcthod of determining the absolute Dimensions of an Algol Vari- 
able Star" in Monthly yotircg^ vol. IxTi. No. 3. 

The Camej^ie Institution of Washington has recantly issued 
ReK'ircfief in Stellar Photometry, made chielly iit the Yerkea 
Observatory, by J. A. Pnrkhorst, duriuf; the years 1894-1906. 
This work refers to 13 variable stura, 10 of which may be called 
i-ecoDtly discovered stim. The object proponed waa (1} tha 
accurate deternimatioii of the complete ligiit curves, and {z) the 
behaviour uf the van^blos du^iIl^ thvir faint stages. The tiuitiber 
of visunl observations IB 1405. Special attention has been givvti 
to the mignituiles of tiie comiiariaon stArs which have been 
ascertained from photometric meu^uit-'s. With each star are ^iven 
plates allowing the magnitude i:urve, the light curve, and the mean 
light ciitve J also a vt^ry clear chart of the viciuity of the variable, 
showing all tlie fttais in the tield, the comparisxtn stars being lettered. 
The work was done with three different teleacop«M», of 6, 12, and 
40 inches uperturf. The breiik of continuity in the visual observa- 
tions resultinjf from the use of theae three instruments " wos kept 
within limits by the use of the photometric mugnitades of the 
compariBon stars." The work must occupy an importimt place in 
the research in the long-period variables. A point which strikes 
one is that the fij^-urvs representing the light curves might have 
bpen more opene"! out, t.^. the ratio length representing magnitmJe 
to t^at of time btring made gn^ater, by wbich the luinur lluctua- 
tions superposed on the niaiu curve would have been rendered 
more apparent to the eye. 

Vol. KV. of the Memuirs of the British Astronomical Association 
has ju»t been published, being the sixth report of the Variable 
Star Saction, by Col. £. K. Markwick, C.B. It contains in detail 
5717 obaervations of 26 well-known long-period and two irn^^lar 
variable stars, made by tweiity-ono meniUTS in tlie y^ara 1900- 
1904 inclusive. There are appended plates showing al a gUnco 
the liglit curves of the^e surs, as deduced from liie iibservulions 
drawn on the Rcale — Icn^^h rflpreiii*nting one magnitude (ordinate) 
-^ that representing 30 dayx (abscissa). Tlie Ibeuretical curves are 
also given, so that the dilfKrence " 0~C " is readily visible to the 
eye for any updcilied date. B- B. M. 

Stellar Spectroseopif tn 1906. 

Nebula. — The apparent persistency of unalt«red form in some 
of the large gaaeous nebulie has frequently attracted nttenttoD. A 
great part of the luminosity of such oebnls is recognised as being 
due to the glowing of hydrogen, helium, and another unidentiSed 



284 



Jtepart of the CowneU to the 



Lxm.. 



vapour. In a chftraclerietic note cnntribated to the Ohurraiof^ 
{October igo6, p. 380), our of our honorary meuibeni. Miss Ai.'do 
M. Cterke, whose receut death is dsfilored in a circle far widtt 
tbau that, of uur uwii Society, has snggested an attempt to brini; 
the work of ibe pliytiiciNtA, J. J. Thomiion, Ramsay, and. Rntberfonl, 
into lina with tlie observatidiia of .iBtronomers. 

In the nebula near jt and S Scorpii rfi-.ftiitly phutoj^pfaei i^i 
Profesftor llarnard on Mount Wilson {AsiToph. Jour.^ xxiii- 144). 
most of the larger stars involved have sEiectrti of the Orion tyyt, 
with the characloristic absorptioti liaea of helium. 

New Stars. — A stor, exhibiting; the photometric peculioritieB of 
a Nova, hai* been liincovered by Miks T>«aTitt at Harvard Colle,:* 
Observatory. Profaeaor E. C. Pickering, in announcing it {Aif. 
Nach., 173, 295, H. C. 0. Circular, No. 121) aa Nova VelomiK 
UJ8 that it is not impossible that it may again become sufficieoUj- 
bright fi)r its opectnim to he obtnimtd, and adds that *' evea witbooi 
Buch proof ther» can be little doubt that the object obsenred i» 
nctuully u Nova." 

The spectrum of Nova Agtiiloj No. 2 has beea observed hj\ 
Mr J. U. Moore at theLiok Observatory {Actroph. Jour.^ xxiii, a6i). 

ClasiijU'xUian r>f SfpJlar Spectra. — The published notea 00 ihi« 
branch of the subject during the year relute almost entirely lo tbe 
relation bi!twet<n the tipcctra of sun-iiiitits and stars ; a study «f 
grcut iuiportaucu, and liki'ly to throw much li^ht on metbodi of 
claasitirotion of stellar spectra. The following papen may ht 
noted : — 

" Spectra of auii-apota and Arcturva" W. S. Adamfl (JrfmpA. 
Jour., xxiv. 6g). Attoution should also be called to Sir K. Lockyer** 
paper {Proc. U.S., Ixxiv. 53). "Spectra of «un-apots ami Tiiiri 
tyj»e Star-s," G. E. Hale and W. .S. Atianis {Aetrojth, Jour., xiii'. 
400). " Spectra of Bim-spots and Fourth type Stars," \V. M 
Mitchell (ihid. xxiii. 211). "On the relation between Stdlv 
Spectral types and the intensities of certain lines in tbe epectra," 
S. Albrecht {A*itropk. Jvur., xxiv. 333V " Kchanced lines of Iron 
in the region F C>" A. Fowler <.1/. iV., lUA.S., Ixvii. 154). 
*' Preliniiiiary ]>apr on the cause of the characteristic phenomcaa 
ofBUn-spotspectra," G. E. Halo, \V. S. Adams, H. G. Gale {Attrvjfk. 
Jour. ). 

llere also we may note a paper by Mifls Agnes Clerk« — 
probably the latit written by her before her deatli — on BU0-6pul 
epectni {OhKrvatory, January 1907, p. 55). 

Studies of Special Stars. — At a time when the maximuxD ta 
the brightuoss of o Celt is shown by Father Sidgreavee (OAwmo- 
tory, Januiiry 1907, p. 49) to be a^ain accompanied by axtreiw 
hrilltanct* of the hydrogen linea, aiid by peculiar behaviour of tbe 
H^ line in particular, it is of interest to p'curd Profewor Frost'* 
observutious'of Pleiotte {Astrvpk. Jour., xxiii. 268). The hydrogos 
lines in Pletone have been frequently seen bright and naiTo*r«j 
Buperposdd on broader dark line«. Froat now observes that 



Feb. 1907. EigJdy -seventh Annual General Meethtg. 285 



bright linigs are no longer visible. Professor Pickeriiijj cnrrobar- 
ates litis observation in 1906, at any rate with rexpact to H,), 
which was uftuii racoixled aa bright in 1896. 

Sir X. Luckyer haa a notu in tho Proc, R.S.^ 77» 5S®> •*** 
peouliaritiiw in the spectra of a. AmlrotmdeP, $ Aurv/x, a Canum 
Ven., and < I'r/x Maj'oru. 

H<!rr Lmlenciorfl {Ag{. Nock, 173, 1) publijthea remarks upon 
the Hficctra nf II. Coronx Horsalu, 12 Canmn Ven., and 72 
Ophiu^hi, The first-named star hoA a spectrum simikr %o that of 
a Perse f, oxtwpt that thu Hyliiie seems tu be ab»oiit. Professor 
Frost corroborates the absence of the hydrogen linoH iti 1903. 

A list of 34 startt with peculiar apectra is f^ven by Professor 
Pickeruiji; {S. d 0. Circular, No. no, and Axt. JVacrA., 171, 139, 
AstTojili. Jour., xxiii. 257). Jieferenue is here mado to Ji Cyguiy 
which is also the subject of a not© by Mii»s Clerke in the Ohgeroaiory, 
April 1906, 

Radial Vdodty of Start. — In a note on sun-spot lines iii 
spectra of Red iStars, G. E. Hale and \V. S. Adams give paren- 
thetic-ally the velocity of a Orionu + 267 kni/sec. {Antrop/i. Jour., 
xxiii. 402). 

Variable Rcuiial Vdocify. — Notes on variability of velocity are 
given for the followinjr stars :■ — 

(The numberH pretixod in the first column refer to Campbell 
and Ciirti.s's Firat Catalogue, L.OM-t No. 79. Here also it may be 
remarked that Professor Campbell givea (i.(>.J5. No. 107) a list of 
chanffes to bo made in the lii&t catalogue.) 



Ludeadortf 



Horttnann 



Zarli«lleii (Bona] 
Frost 



29 I Auriga 
80 ■ Urttfonia 
12 Artetis 

y Ca&stoiioin: 

kz CaaslopeiK 
65 Loonis 

•Orioiii* ^.\>. 
- I* 1004 

39 CanU Mftjorifl „ 

3o(r)CaniaM^'ori« „ 

uClrionin ,, 

T Honoc»rotu „ 

80 a Draouiiis „ 

129 jSOptiet „ 

t Oeuiiuomm Cain|i)m11*iiil Moore 



" Ophiaclii 

(OnipwC.7579) 
I SagitU* 
•iCygni 
Cygui 
(fCygiii 
. 1 Capruorni 




A A. Nach. 171, 49 

171. 127 
.. 171. 149 

173. '*5I 

17.1. loi 

173. 353 , 
AarojA. Jour, zxilt. 204 

„ „ 265 (footnote) 

.. ., a66 

■I M 267 

„ miv. 259 

Pub. A.S.P. 18, 30S, and L.O.S. 
No. 107. 



Hoddrill 
Wright 



Pub. A.S.P. 18, 252, tod L.O.B. 

No. 107. 
LO.B. 107 



286 



Beport of the Council to the LXVtL 



a Unm Mioorif 


CuapMl 


L.0^. 107 


(Poluis) 






fEetirali 


Wriglit 


It 


m V«1oniin 


II 


■ I 


F Cenl»uri 


• I 


<t 


«aC«DUim 






t CKprioemi 


Slii>b«r 


Attroph. Jour. xxiv. 361 


T Unm Hiyorii 


Moon 


,. xxiii. 363 


AHydw 


■1 


»» ri 


^ Ur^K Hajoru 


(1 




y OphiDehl 


Albrwfat 


Puh. A.S.P. 18, 66 


AqnUv 


It 


18, 142 



OrbUs of SpeetrOMCiipie Binarin. — Tlie binary cborMter of 
the fainter companion of CaMor wits discovered by BeJopoUkr 
in 1896; Ilia l;iter wurk led liim to the view tbat there wu 1 
rotation of thu line of apsidea. The obwrratiuiis itiai^e at Ui^ 
Lick Ob-^ervatory have been folly diacoBsed bj Mr H. D. Curtis 
{Atiroph. Jour., rziii. 351}, and he is led to atmndon lJ>e 
assumption of any rutatioo in the line of apsides atid to adopt un 
orbit nearly circular, — 001. In October 1904 Mr Curtii 
auomiQced the variation in the radial velocity of tbc bri^ht«r 
component; iind he dMluc«B fnr it an orbit which exhihiis si^ 
of L-ansidemble eccentricity, £ — 0*50. Doberck, in hia lust discuf- 
aion of the vinual aysteai, arrives at the concluuiou thtit tlie ppnod 
347 y<*r9 is UiB imwi prolwble. Tbe relatire motiun of the t«oj 
component eysteins derived br Mr Curtis is 714 km/sec. ; aud 
periods are 9*21 SSdayit and 39383 days for tba bright and the f&intl 
componpnt» respectively. Mr Curti» has searciied for Tariahitity la' 
the light of tbe brighter component, but has not detected any. 

Krom a disciiHStoii of mdial vflocities dt^iluu^l at the Lick 
Obserratiiry from 56 photographs of the spectrum of X AmiromHiai 
Mr K. Bums has calculated an orbit with a pt.-riod uf 2*05 dan 
{Atiroph. Jour.^ xziv. 345). Further (il>aervatiuiiB am required ta 
decide whether there is a change in the elements. 

Radial Velociiirs frtym Objective /Vt«n.— The importance of 
devising a wliolesalu metho«t of gathering information about radial 
velocities is wiiltdy recognised. Three notes on practical eugget- 
tions have been inado in the last year. 

I*rofesaor K C Pickering {Astroph. Jour^ iiiii, J55) rvoalls the 
method BU)(g(^te<l by him in Harcard Circular No. i3~'two 
exposures with the prism reversed. Mr G. 0. Comstock {Ai4ropk, 
Jour,, xuii. 148) suguosta the use of a single objccl-glass wit^ a 
direct- vision objective prifim in front of each half of the object- 
glass, the prisms being hxad irith their nfracting edges in oppusit* 
directions. 

Mr De Lisle Stewart {Aflroph, Jour., xxiii. 396) deecnbaa 
a form uf instrument with two objcct-glasflas, raob having an 
obje-'tive prism in front of it; by acproprinie inclinatiuu of tfaa 
axes of the lenses, and by separation of their centres, the Li 
spectra may be set aide )<y side ou one photographic plate 
opposed directioDs. 



feb. 1907. £ighty-aevtnth Annual Octural Meeiinff. 2S7 

Sedttdion of Ohaervations. — Dr H, K. Palmer (Astroph. Jour-, 

tsiv. 51) contribute-a a Dote on a short method of comimtiD^ nti 

ipproxiinata value of the reduction to Sim in radial velocity 

leterminittions. Dr Hartniann (Ast. A'uc/i., 173, 97) remarkti 

ijioti tlm uioihuJ, Bugk!uj!t<j tlm utili^iatioii of the dltilance vt tb^t 

[atar from the apex of tlie Karth s motion, metisiire'l on a gri.?at circle, 

lend doAcrilie^ a practical method of obtaining the reqiiiriH) result 

rby r«.'Ldiug8 from n globe. B. r. ». 



I 



I 



The Astrographie Chart and CataJoffUP, 

There is little tu roctjrd in coDiicction with thu Astrographic 
Chart beyond what may he gathered from the I'roceeilings of 
Obaervutorios id another part uf tbiii report. The piiblicaliuD of 
the uifasurea of stars of the northern zoiiea 'n* progressing'. Tho 
printing of the rectan<,'ular co ordiuates of the Greenwich Kone, 
Dec. + 64' to the Pole, in practically complete. Oxford University 
ObitBrvator)' ha« publishud it^ Hrdt volamit of mt'axtirea Dec. + 29* to 
+ 31*, a second volume Is on the eve of publication, a third is Iwtug 
priiitfd, and five uiotl- vuluuies will complete the Oxford section. 
Nothing' has issued from the French obiM^rvatoi-ie-'t during the year 
1906, although the work of publication already begun at Paris, 
Bordeaux, Toulouse, and Algiers is no doubt proceeding. M. Loewy 
lueritiuned in hJH »iiuu»J re|>ort that the work at PariH had becu 
dtihiyed by the di-ath of M. Paul Heury, and possibly the death of 
M. Itayt^t at iiurdeaux hoa caused n similar hindrance. M. Kenry 
has bi^en succeeded in the snperintendencB of this branch at Paris 
by M. Puiseux. 

Three volumes were pubtisheil from Potadiim in the years 1899 
—1903, and it uppoara that four more volumes of measures were 
prupartni fur prtnliug some tliue »go, but the pulilication was 
delayed by the computation of the pi ate -constants. As to the !u>ne 
47' to 64*, which Ih dividtwl between the Vatican Obwrvtitory at 
Kome and the Catania Observatory, uothiu^ has appeared since 
the first voluoie was issued from Borne iu 1903. Father Hagen, 
thn newly appointed Director of the Vatican Observatory, paid a 
vidit to OrKenwicli lust summer for the special purpose of making 
himself acquainted with the details of the astrograpliic work. 

Of the zoiiea whicJi cover the sky south of the equator,* that 
between Dec, 32" and 40' undertaken at a later date than moat 
of the other*! by the Observatory at Perth, West Australia, seems 
to be making small progress. The staff of this obsorvatury is 
evidently inaJequate to effect the measurement vt the plates 
unU-ss some othor wurk of the observatory is discontiuued. The 

* DiDce th« above tias been in tyyv a loltvr has been recaivcd from H. 
Tallc, Director of thu Taciihaya Obs<->rvktory, Mvxico, uvijig that 1200 of thi> 
1260 cattlogae plnt^s rw^uinxi itt cover thp wiic - lo to - i6' Lsve buen 
tnltiia. «nit that tho cdinputation or tbit pUlu, docIiDstivn - 15° snd - 16*, 
buCnittin R.A. c^ BnJ ^*', will be ooiupletn)!, urn) thf ifnulUi ^iriotad ia % (tm 
weeks. Some progies* has alio boon made in talniik" ib« cHuV v'^^'vok 




288 Report of the Council to the LXTtL . 

exact »taUi uf tho work betweeu this roue auil tlie soutk pole w31 
be learned from the reports of tbe British Colonial Obserratoritt. 
A Buggestion haa hecii mside that another conference sfaooU 
be held at a neur date ; alionld this take effect, infonnatioB 
Katbcred as to the (lotiitiun uf afl'nii-i at nil the observatories mifbt 
indicate auj rearraopemcHtw aecesstirv to brinj: the whole wufk 
to a conclusion, and discuseion migrht lead to resolutions && to tbf 
procedure nhich should iViUow the publication of the meutiureB. 

Enlargements of the Cliart Plates have been viintrihiited duhog 
the yi'ur h}' tho l>irectont ot the I'lirii, Algiers, Touloase, Iiordeuii, 
San Feniiuido, lUiJ Greenwich Observatoriea. The total nnmber 
issned from these uImoi vutorics is now 

Paris 271 Bordeaux 64 

Algiert^ 276 Sail Fernando 95 

Toulouse 12a Greeowicb 53S 

u. P. H 



Star Catalogue*. 

A number of important star catolugues have appeared dortng 
the year. !n thiA note it is only poMible to enumerate liitrn 
and indicate their scope, 

Catalwjw! oj 2!oilutrttl Stars /or 1900 omZ 1930. — "nk 1* 
publiithed as vol. viii. piirt iii. of the ABtronomi^ papers of 
the American Ephenxerin. The catalogue contains 1607 atani, tati 
is [irepar^^d principally for we in occaltations of stars by Uit 
Moon. In determiinng positions of tlie stars and their proper 
motions, the more iiuportaut catalogues from 1755 ^ 1900 hiT<! 
been uso.il, after hein){ ri^uoed to the syAteiu of Xewcoul'i 
Catalogue of Fundumt^utal Stars. This catalogue containa ion 
8tat« which nmy be regarded m ftindamental. The (HMitions U 
tbe remainiler will be improved very considerably by rcnI 
observations of zmliacal stars. 

Cape General Catalotjite for igoo. — This catalogue cootaiw 
3365 slurs wliicb are nurth of the zenith at the Cape and 995 BOtUfa 
of the zenith. The catalogue contains the results of obaervmtwa 
at the Cape of 2798 Jiidiacal stars contained in a liat circolalid 
by Sii' Iiavid Gill, and adopted at the Paris Conference of 1896 
as forming a sultahh' basis for a catalogue of zodiacal stan n 
connection with hrrliometer ohnt-r vat ions of planets, ocooltetiooi^ 
etc. Tlie re]iiaiuder of the stars are, generally BpeKking, start 
brighicr than S"^'5, which are not found in any catalogae of 
precision. The stars aro generally observed fiv^ times, the epoch 
being about 1903 or 1903. The right aflconsions are corredoi 
(or personal ecjuation dependin;^' on magnitude. The decUnatiooi 
are reduced to the system of Newcumb's Fundamental Catalogne 

Roiidife C<Ualogue /or 1900. — Tlie lladclifle Catalogue d 
l'JT2 stars continues the programme of the Kadcliffo Calalogiu 
for 1890. The 1890 c&ta\o^fe cotAamw^ iMv. Vjw*. down to 7*^ 



Feb, 1907. Eighty-seventh Annual General Meeting. 289 



I 



I 



fn.im the equator to - 25* dec. ; the pivBant ciitaIo)^ue contains 
all sterii to j^-o between the ctiualor Hiid +5' doi:- A large 
iitiinber of tlie zodiacal stare containecl in the Zodincal (?Htalngue 
of the American JCp/wntrris and in the Cape Catalogue are bIbo 
obiKrved here. Attention may be called to the determination of 
(livot errure, and the new delurminuuou uf the diTi»ion urroro 
given iu the iDtrmluctioa. 

Henderson's Catalvgae/or 1840. — TJif Annais of the EUirtburgh 
Obmrrafory, wl. ii., cooaists of a reduction hy Hr Ilalni of tho 
observntiouK made at the obseTvatory on C'alton Ilill by Henderson 
and bis asKsLant Wallace. The catalogue contains 3595 stars 
from the jmle to dec. -20°, nearly all brigliter than 7"'"o, 
observed betveeii 1835 and 1845 with a transit ioBtruujeiit by 
Re|i»i»ld and a mnral circle by Trcnaghton & Simmc. The 
principal differencea between the new and i>ld reductions are, in 
the ri^bt ascensions, the eliuiiuatii>n ol' the effect uf the beat of 
the illumination' lamp on the level and azinintU, and in the 
dec limit ion fi, the correction for divimnn errore. The [wsitions of 
the clock Btara, etc. are taken from Auwers' Fundamental 
Catalogue. 

AmljTOTtri'g Catalo(/ue of all Siarji iv 6".5 /ur iqoo'o. — This 
ciim|iilatioti from the Catalogues of the As( t'ononmche GeseU))rha/f^ 
the Argentine General Catalogue, and other sourcei', containa 7796 
stars, whuse posltioofl are given to o"'! in R.A. and 1' in dec, 
and may 1>e very useful wliur'd approximute places of bright stars 
are required. 

The catalogUf^ referred tfi al>ove are in tlm main concerned 
with fairly bright stars. The catalogues which follow contain 
fainter stam. 

Cape Catalogue of Astrographic StanJanl Stars for i9oo'0. — 
The piirposi; of this catalogue is to provide accurate positions of 
atars to serve as reference stars for thu Cape Kectiou of tho AkIio- 
graphio Catalogup. It cantainn S560 t^tars between the declinations 
— 40' and -53*. All are observed three tiraos, many nf tlieni 
five tinm>!ii. the observations being all made iu the four years 1S96- 
1899. The accidental probable error of a single obaervaiion is 
given as ±"024 sec 8 in H.A. and ±o''28 in decimation, so that 
the accidental error of a result depending on three or hve observa- 
tions is very smtiU. The point of special interest in the reduutiuua 
is the ftpplication of zone corrections to each series uf obsorvutions 
derived by comparison of 10 or 12 selected stars each night with 
the means uf thvse stars from all observatiouM. ^[agnitU(lo ei|nation 
has been applied separately for each olisf^rver. 

Ex.toii»ivo eompaniioiu are made with uarlicr catalogues, from 
which proper motions of a large number of stars have been 
deduced. Those proper motions depend to a large extent on the 
Cordoba Catalogues, and it is stated that they cannot be used 
for purposes of cosmic&l research without further investigation of 
the ^8t4:matic errors of that catalogue. The pro[>t-r motions at*-,, 
however, sufficiently accurate for the imt»eA"\6,lft ^vw^aefc ol ^J^i^l 



L 



290 Report of ike Council to the Lxnt 4. 

catalogue, which is that of furming u secure foandatioii for iIm 
Ca|)6 Section of the Aslmgraphic Catalogue. 

Antronamiefhe GuftUefiaft Catttloipte {attd Section), StroMtlmry 
Zone. — This catalo^'ue, which fortna the 6nt division of the A. (i. 
Suutfaeri) Catalogue ( - 2" to - 23'), extend* from dec — 2' Ut d«i 

- 6". It contains 8204 stars, being all tht; stirs to 9*"'o and fuotrr 
ones according to the A. U. prograuuDe. The positions an girtH 
for 1900*0 (not i875'o as in the N. Section of the A. G. C), w>d 
are rednced to the «_vst«iu of Auwera' Soothem KtiiidumeaUl 

Ltalogue. The average uumber of obsenatioua on which 1 
ilo^ue place ■lt;[ietids is UL'arly three, and ihe probable envn 
about ±'o2i and ±o""i7, being uniform iu declioatioo for 
all ma^itadedt, but in right a»cenRi<itis ranging froru ±**oi7 fb) 
bright stars to ±'024 for these fainter than 9'"o. 

Aflrotwini^he Oe$eiUc}ia/t Ckttalogue {znd Seeiion), TTto, 
Ott.a/:nng Zone.^TUiB catalogue, forming the second ilivi5toD of 
the A. ft. Southern Catalogue, was publishbd in 1904, but hu 
not yet been referred to in the Council reports. It extends fmni 

- 6° to - id' dec. and contains S46S ttora. The probable acci- 
dental error oeeaia to be about the some as in the ^iraaabor^ 
Zone. 

In this connectiim it may be nnticed that the reductions of ihf 
obBervHtion.1 fur the remaining z'lnes, Caiubridge U.S. ( — 10* to 

- 14'), Washington ( - 14' to - 18"), and Algiers (— 18* to - aj'), 
■re being rapidly pushed forward. r. w. u 



Unit'ertal JHme* 



I 



r 



Smce the last mention of the subject of Universal Time in thii 
Beport (1905 February), the time system of India has been alterad 
as theru indicated. From 1905 July 1 the standard time (^ 
India has been 5^ hours fast on Gre^^nwicb, that of Burmah 6j 
liours fast, but the time-ball of the Colaba Oliiservatory, Bombay, >• 
dropped at exactly 5** a.ni. Greenwich time. 

It has butiTi enacted by the Council at Port Louie that from 
1907 January i the standard time throughout Mauritius and its 
de|>endencieK shall l>e the time o£ tlio meridian sixty degrees east tif 
Greenwich, except for the Cbagos archipelago, where the etaudard 
lime 5 hours eitst has been adopted from the same date, 
time 4 hours fast on Greenwich is now also standard in the col 
of the Seychelles. U. P. B. 

Chodttjf. 

The new graviuietric Survey of India, begun in 1904, is sttR 
proceeding, and some resultii of n preliminary nsture bare Rppeued 
during the Inst two years in the puhlicatmnB of the liuval SocietT. 
The history of the subject of gravity in India begim^ ia the t«^ 
1565, iHitween wVicb ^«at &n\ v%-\i, olnibtvations were mode 




[Feb. 1907. Eigkly-scverUk Annual Oe7teral Meeting. 291 



f officers of tho Survey at 31 slattouB in India with the Koyat 
Society's iuvariable seconds pt'ttJitluras. Tbe reaults of ihexc 
operatitme showed coiifiidf^mbte diKRonlances fn>in the values of 
gravity as cumjiuted by Clairaut's law, aud their physical maauiHg 
was for MUtTiti titiju a mattur of dUcuitsiuu. At 15 inland stations 
uudur 2000 feet abuve sea-level the number of swings of a 
"jtecuiiJa" pendulum was 2*27 I«s per day than that computed 
from theory. At 4 statioos Vjetwoen 2000 and 7000 ft-ut htgb the 
defied wa8 HB muoh as 5 09, nnd ut one .ttation, in the HiuialayaiL 
table-knd, 15,400 feet abovt Kwi-leve], die invariulile pendulums 
mudc 21A swings per tiay less tbnn was expects*!. Tbe dclioieticy 
of gravity which was then fuund tu exist in HinialayuQ regioDs was 
at-lributed by different authorities to different causes, bat lately 
there neems to have been some doubt as to the actuality of the 
fact itself, fur at the Intcrciational Conference of tbe Ueodettc 
Asauctatiott at Coputibageu in 1903, a resolution 'was passed for 
aubmission tn the Government of Imlia to the effect that it wrs 
desirable to make an accurate dtiterminutiun of the distrihntion of 
gravity in the niounUiinnus cimntry and in the plains of India. 
Tbifl work was begun in India in 1904, with a »et uf half-second 
peiidulum» of the Von Hteriieck pattern, which were previounly 
swung at Kew in 1903, with the primary object of standardising 
the instruments. As, however, on the suggestion of the Astronomer 
Royal, a series uf Hwing^ were also made at Greenwich, the resnlta 
gave a diflfereuco of tbe value of gravity at tbe two observatories. 
This observed difference* of 0'0i4 dynes excess at Kew is rather 
larger tbnn the theoretically computed difference, which is +0*005 
if the corrections for tbe kuown geological strata around the two 
places be included, but the accordance between computed and 
observed is neurcr tbnn in previous detenninutious made with the 
older form of instrument, and tlicre is close ngreeincnt between 
two sets of operations that have been made with half-sL-cond 
poiidubimi). 

The re»ullB found in India by Major Ijenox-Conyngham, so far 
as yet published, f are renmrkable. At Bebra Dflu, Madras, 
Bombay, Munsooree, the force of gravity, as recently detvnuined, 
U larger than the earlier value by a considerable quantity, so that 
Cf^Iunel Iturrard feels justified in saying that " the idea that gravity 
is eiceptiouaily wt-ak throughout India as compared to Europe can 
no longer be upheld, nnd the so-called marked negative variation 
has been found to rest on err<meoiis data." 

The same memoir in the Pki!tu*o]/hii:ai Trojuartums contains an 
account of observations made to dclcrmiiie the local deflection of 
gravity over India. An earlier publication X ou tins subject 
showed that local deflections of gravity could be clasai&cd in 
groups, and to teat this, observations for latitude have been ma<le 

■ Proc Sioj/. Sof., 1906 November 5. 

t " On tbe InleautT and l>ir«otioD of the Force of Gravity in India," by 
lieut.Col. Burraid. R.K., F.R.S., Phil. Tram. 1905. 

X Survey uf India De)iartiDeat, ['roTcssiDuai Pa\tet Kq. V i^^- 




292 



Report of the CqumoU to tkii 



LITn.4. 



uader Col. Btirrard's direction at various stations along a metidiia 
or rather along each of several rn«ri<lianSi with a reAUlt which pro«ed 
tu b« verj' much tut expected. lu the mountainous regions of t^ 
Hiutalaymi the plumb-line in deflected northward by mon than 
30"; in the pluius the deflection is in the same cUrcction, bat much 
le!» in amount. Further south, and piirftllel with the Himaiajw, 
18 M trai-'C of country 4000 miles long and 200 broad, wber* tba 
phiinh-line is deHec^te<l in the opposite direction, i.<^ towards tha 
south ; ami having; pn^taed througli that zone of «ontl)erly dcAectidO 
into the Itidi[i)i peninsula or into north-west India, the phtmb-luic 
is ugntn found to bo dtillO'Ctcd northward. Discusaing lluM 
determinations, tlie con r.l us ions are arrived at that there is a loal 
deflar?tiun of };*iavity at Kulianpur, the origin of the Siirvoy, and that 
a HpLeroid which Las the elHpticity of Besael, 1/299-15, bnt tlte 
»oiol-m«j'.<r-axiB found by Col. Clarke, 6,378,190 metren, )>est re- 
presents the fact« of Indian geodesy. 

Deiails of the geodetic work done in Soath Africa will be 
found in the report of the Cape of Good Hope Observatory. It 
apptraru that the measurement of the uiertdiau 30' east, ol 
GretMiwich is complete, or nearly 30, as far north a» lacitude i;' 
58' S. Ai.d honi it may bo mentinned that the Survey department 
of Egypt, under the directorship of Captain H. G. Lyons, I^*-Sa^| 
F.K.S., haa b(-gun the preliminary work of the geodetic triaeguli^l 
tiou of Egypt, wbich it is hoped will ultimately be cunnected witk 
the tiiangulation in tbe southern part of tbe ContineDt (an ioto- 
mediate Hoction being measured by Oermany), and ao complete tba 
measurement of this 30th meridian from 34' S to 30" N. 
Captain Lyons say» in his Report for 1905, it leenia only fi 
that the country where Kratostbenee (ac. 275-196) did the 
geodetic work, Bbould take a share in tbe modern ro-^e 
tion uf the earth's form. 

During the year a volume has been published by 
Astronomer Royal containing tlie details of several de term! nation 
of ]L>n^itude made by the Greenwich staff in the years tS8S— 190}- 
The results given in tho first part of this, the diiTurence of longi^de 
between Grer^nwich and Paris, have already appeared in tbe 
MantUy yoticcjf. The second purt comprises tbe deteruiinalion 
<j| a trans- Atlantic nrc, Greenwich-Montreal, and the tueaaurem 
of the arcM bctweeu Greenwich and Watervillo and Killorglin 
tbe south-wei^t of Ireland, which are of some intere&t. This [xji: 
of the United KIngilom is of geodetic imjiortance, since it focntt 
the western end of the great European arc in the parallel of 
latitude 52* N, and in the middle of tlie last century three eepatmte 
determinations of longitude agree*! in abowiiig that the astronomical 
vulue of tbe arc was greator than the geodtitie when Clarke's fim 
Talue** (fl = 20,926,^48 feet, 'j= 20,855,233 feet) were used for the 
upherntd assumed Co represent the Earth'» aurface. The fiuggastwa 
was made at the time, that the difTerence wae due to local attraetioa 
at tbe woHteni stations, hut the amount war; larger than was con- 
sistent with any teaaonu\'>\e Vv^-^^Al^eai^. Tbe new detenniuations 




oint^ 



•"eb. 1907. Eighty-iettnth Annual Gentrai Milting. 293 

oontinae to 8huw the astronDiuical value greater than the geodetic, 
' thu same spheroid (u before being ossumcil in the coiii]>ulaLiou of 
[the latter, but the diirerence is not «t> large. Tlte pxcess in the 
[case of Waterrille ia ©".jy, in the cage of Killorglin +o*.i5. 

In a short pa[>er* on the »\7M of the Karth, Professnr UtOmert 

[cumbiiios the values of recent arcs which connect Greenwich with 

[the CoDtinent and the arc Oreenwich-KUJurKlin, with prevloua 

[diHcuBsiiirie of llie great European ore, and arrive^ at a correction of 

-t- 660 metrea to the n found l»y BaiBei ; or, in other words, the 

[derived eqttaturial radiuit of tho ^^^th iit 6,378,057 mevreA, or 

30,925,572 feet. Professor Helmert ^ivea this result with bowc 

reservation, ajiparently with reference to the fact that the question 

of local attraction at the Western station^) bos been treated only 

by an appmximate motliod. 

The triennial Conference of the International Geodetic Asaooia- 
tiotiB was held in 1906 ut Buda Pest; the subjecta of the oieasure- 
ment of the arc in Pern by French Geodesista, the survey of 
Africa, and Indian geodesy formed part of the proceedinga 
Sir George pArwin expressed the wish that it might be possible 
fc<> hold the next meeting of the Association at Cambridge, regretting 
that it WHS not in his power to do more than make the 8ug^i.-stioii. 
A formal invitation to l^ngland must proceed from the British 
.Government. a. p. a. 

' "Die GroHC der Kd«," Sitaung^imehU tUr K6niylitik Preusritchett 
'.Akademicdar Wiuemmhajim, 1906, xxvU. p. 533. 




29A 



Ziat 0/ Fublie Instituiions 



txnn. 



~Ll8T OP PrBLlC InSTITUTIOtTS AND Of PbRSONS WHO HATS COT 
TRIBITED TO THK LmRAAV, KTC. SINCE TOH LA«r ANSU'EItt**! 

HJH Majf^sty's Governmeut in Australia. 

His Miyt'sty's GuviTimient in India. 

The Lords CommiMiniiere of the Admiralty. 

The French fiovorninent. 

The Italian Government. 

British Asiiociatiun for ilje Advancemeat of Science. 

Ilritiah Astronnmical AsgociatioD. 

Britl-h Il<»ri]l[ij;U'al Inftituto. 

British South Africu Compauy. 

lleoluyicul Society of London. 

ileteorulogical Office. 

National Phy«ii»] Laboratory. 

Oliticftl C'oDveiition. 

PhjHtcal Society of Ijundon. 

Royal Gui^graphical Society. 

Royal Institutimii of Great Britain. 

Kiiyai Mftteorolopical Society. 

Royal Observatory, Greenwich. 

Royiil Photographic Society of Great Britata. 

Royal Society of London. 

Koyal United Servico Institution. 

Society of Arts. 

Solar IMiysicH ObHervatory. 

Uiiivereity College, London. 

Belfast N'dturul liistury and Philoeopliical Society. 

Bir[t)in-*li)itti ini.-I Mi'lUiod Institute Scientific ScKiety 

Cambridgp (>h»er\'atijry. 

CaiiibridgQ PhiloBoph'tcal Society. 

Cardiff, Astronomical Society of Wale*-. 

Challiutii, Uiiyul Kngineers' Institute. 

Dublin, itiiyjil Irish Actademy. 

Dlihlin, Royiil Society. 

Kdlnbnr^h, Royal Oljservalory. 

Edinhurxh, Royal Society. 

Galway, (^ueenV Oollej;e. 

Leeds Afttronomical Society. 

I^ifds Philosophical and Literary Sociciy. 

Liverpool Aulroriomical Society. 

Livorpoul Literary and Philosophical SiHsiety. 

Liverpwd Observatory. 

Mancb^ler L\letM5 aui 9Vvvli«.ovhical Society, 



Feb. 1907. 



and of J*eraom, etc. 



395 



Itfanchcster, Mauicipiil School of Technology, 

Oxford, Radciifft? Olwervatory. 

OxfonI, Univorsily Observalopy. 

Rtiyby School Natural History Society. 

St4Aiyhurpl College Obeervatory. 

SoutLjjcirt, Feriiley ()l»ervatory. 

Tniru, Koyal iDstitution of Cornwall. 

AMwidia OI'Hcrvfttory. 

Adelftirle, OoTernment ObscrTatory. 

Algiew Observatory. 

Amsterdam, Boyat Academy of Sciences. 

Arrotri, Royul Observatory. 

Ath«iiB Observatory. 

Auittralu^ian Aiuociati<m for the Advancement of Science. 

Basel University. 

Basel, Society of Scieucee. 

I^itavia, Royal Magnetical and Meteorological Observatory. 

BaUiTia, IWal Siioiety of Sciences. 

Berlin, Genoan Physical Society. 

Berlia, lui^Utution of Computation of llie Royal Observa- 
tory. 

Berlin, Royal I'riiAtiiao Ai-adeniy of Sciences- 
Bologna, Royal Academy of Sciences. 

Bolo>fDa 0b8er\-atory. 

Bombay Branch of tUo Hoyal Asiatic Society. 

Hombay, Oovernnietit Observatory. 

Bordeaux Observatory. 

Bordeaux, Kociety of Physical aud Natural Scieiiceti. 

Boatoa, AiJiericuii Acaduoiy of Arts and Sciences. 

Brazil, Sooiedude Scientitica de S&o Paulo. 

BruMuls, Belgian Astrotioiuica] Society. 

Brussels, Royal Academy of Sciences of Belgium. 

Buda-Peslh, Hungarian Academy of Sciences. 

Budu-PoHth, Koyiil Huncarian Institute for Meteorolo;^ 
aud Terrvatrial MagnetiMii. 

Calcutta, ^Ifliiitic Society of Bengal. 

Canada, Department of Marine. 

Canada, Geological Survey. 

Cauada, Royal SociBty. 

Cape of Good Hope, Royal Observatory. 

f'ape Town, South African I'hilusopbical Society. 

Catania, Italian Spectroscopic Society. 

Catania, Koyal Observatory. 

Colorado College Ubaervatorj. 

Copenhagen, Royal Uaniah Academy of Sciencov. 

Cracow, Academy of Scieoees. 

Belfl, Geudetic CommissioD of the Netherlandii. 

Dijon, Academy of Sciences. 

Kgypt, Survey De|»artment. 

Geneva Obeervatorv. 



igiS 



List of Public InstUiUions 



UiML] 



GotUngen, Royal Obgerratory. 

Gfitliogci), Royal Society of Seiences. 

Granada Observatory. 

Gioningen, AstrouomicAl Laboratory. 

Hdle, Imjwrial lipoid -Caroline Academy. 

Hamljurg Observatory. 

Harvard College Astronomical Ohsenratorj. 

Heidelberg, A.strophysieal Observatory. 

Heidelberg, Aatronotnical Institute. 

Hehingfors, Central Meteorological Institute. 

Helsiii^jfors, Finnish Society of SciencM. 

Hong-Kong Obaervatory. 

India, Survey Deimrtment. 

Inti^mational Dureau of Weights and Measures. 

KaBan, Imporial University. 

KodaikAual Observutory. 

Leipzig, Astronomical Society. 

Leipzig, Prince .lablonowski Society. 

Lfiipzig, Royal Society of Sciences of Saxony. 

Lick Observatory. 

Liabon Obsurvatory. 

Lowell Olieervatory. 

Liimi, Astronomical Observatoiy. 

Madrid, CiBogrephiral lustitnte. 

Mailrid ObBervatorj'. 

Madrid, Koyal Academy of Sciences. 

Manila, Pbilippiiie Woather Bureau. 

Manritius, Royal Alfred Ohaenratory. 

Melbtmme Observatory. 

Mexico, Scicutifi^: Society '* Aiitoaio Aixat«." 

Missuuri University. 

Moiicalieri Observatory. 

MoDtpelMer, Ftnmmarion Astronomical Sociefcy. 

Moscow, Imperial Society of Natiiralistn. 

Mount Wilson. Solar Observatory. 

Munich, Koynl Bavariau Academy of ScienuaiiH, 

Munich, Royal Observatory. 

Natal Obaervatory. 

Naples, Royal Academy of Sciences. 

NeucEiftte! Obficrvatory. 

New York, Columbia College Observatory. 

O Gyfl.!La, Central Meteorological and Magnetical 0\ 

tory. 
Oporto, PolytocUnic Academy. 
Paria, Academy of Scionces. 
Paris, .\fltronoini(;al Society of Franco. 
Paris, Bureau of Longitude. 
Paris, Ecole Polyteclinique. 
Paris, >latVi*jma,tka,l Society of Fmnce. 
Paris Oljaetvwlory. 



Feb. 1907. 



and of Persons, etc. 



297 



Parifi, F'hiiomatbic Society. 

PennBySvaniA University. 

Perth Observatory, Weatern Anstralia. 

Philadelphia, American Philonophical Society. 

PhitiKlelphin, Kranklin Institute. 

Philadelphia, Univeraity Observatory. 

Pola, Imperial Hyiirographic Office. 

PoLadam, Astruphyflicai ObHervatory. 

PotedaiD, Central International Geodetic Burttau. 

Potsdam, Ruyal Prusbian Geodetic Institute. 

Poughkeepsie, Vassar College Olwervatory. 

Prague, Imperial Ohaervatory. 

Pulkowii Observatory. 

Piilkowa, Physical Observatory. 

Qiie^-nslftod Government. 

Rio de Janeini ()b«erv.itory. 

Rome, Ro;al Academy dei LirKei. 

Rome, Valicau Obsitrvatory. 

St Petersburg, laiporiul Academy of Sciences. 

San Fernando, Observatory of Marine. 

San Franci^oo, Astrotiomioal Society of the PaciUc. 

S phia University. 

Stotkholm Observatory. 

Stockholm, Royal Swedish Academy of Sciences. 

Stockholm, Swedii^h (ieodetio Coramissiun. 

Sydney Observatorj*. 

Tacubayii Xational Aatronomical Observatory. 

Tokyo Astronomical Observatory. 

Toronto, C'&narlian Institute. 

Toronto University. 

Toiiloufie, Academy of .Sri«ncea. 

Toulouse, Mottwrological Commiaaion. 

Toulouse Observatory. 

Turin, Royal Academy of Soipncee. 

Transvnul Meteorological Department. 

UckI*;, Royal Observatory of Belgium. . 

United .StaU-9 Coast and Geodetic Survey. 

Upiiala, Hoyal Society of Science*. 

Vienna, Austrian International <t(>oiletic Commiaaiun. 

Vienna, luiperial Academy of Sciences. 

Vienna, Im[>enal Military Geoifraphic Institute. 

Wan;.tinui Astronomical Society. 

Warsaw, Observatory of the Imperial University. 

Washington, Knreau of Standards. 

Washington, Navy Department. 

WaaUinglou, PhiloKuphical Society. 

Washington, Smithsonian InRtitiition. 

Washington, l.^nited States Xaral OhRervatory. 

Yale University A.'ftronomical Obaervatorj. 

Yerkes OUserval^ry. 



298 



List 0/ Pubtie InsdtiUuMS 



XXXXl, 



Zi-Ko-Wei Aatronomicol ObncrTatory. 

Zurich, Ceotrol Meteorological luetitute of Swtn«rUod. 

Zbrich, G^otletio Comtniftsion of SwiLzerland. 

Ziiricb, Natural History Society. 

Editi>rs of ibe " Americaa Journitl of Mathenia.tirjL** 

Kliilors of tbe "American Journal nf Science,*' _ 

Editor of the " AsironomicAl Jourual." 

Ji^litor of the "AslronomiRche Xnclirichton." 

Editor of the "Aatronomischer Jaliresbericht.'' 

Rditont of tbe ** Astrophyaical JournAl." 

Editor of the " Atbeneeum." 

Editors vf the " BtiUetin des ScienceB Halb^iuatiqaes." 

Editor of the " Knglish Mechanic." 

Editor of " Himinei und Erde." 

Editor of " Indian Kiigitieering." 

Editor of " Naturu." 

Editor of *' NsturwJAsenschaftliche Bundscfaau." 

Editors of " The OUervatory." 

Editors of " Popular Astrouomy." 

Editor of " Striua." 



A. Balding, Esq. 

Count do la Bauma Pluvinel. 

M. H. Fioiirget. 

Prof. M. Breiidel. 

Rcrr L, BreaDor. 

J. C. Clancny, li;*i. 

Hugh Clements, Kaq. 

MiM A. M. Gierke. 

T. Colbv, Esq. 

W. B. Dawson, E^. 

M. N. Douitch. 

M. I'*. Kaccin. 

M. M. Farman. 

Herr J. Feiiyi. 

M. C. Flammarion. 

Dr J. Franz. 

Prof. E. B. Frost. 

Mr Henry Frowde. 

Herr A- Gasser. 

Prof, R, (!iantier. 

Sir D. Gilt. 

Rev. A. B. OriraalJi. 

Herr C. Habicht. 

Prof. G. E. Uale, 

Prof. E. Hartwip. 

T. K Heath. 

Prof. R. Holmett. 

Rev. A, C Hendewon. 

ProLG."W.H\\\. 



A. a Hinka, Es-i. 

Prof. S. ITiniT&nia. 

Sir Vi'm. Ha^gin^. 

P. M. .Tones, £sq. 

Prof. J. C Kapteyn. 

E. B. Knobel, Ka^i, 

Prof. E Lobon. 

Sir Gorman Lockyer. 

Dr ^X. J. S. Lockyer. 

Porcival I.AWell, Bwk 

W. T. Lynn. 

V. H, MacEinnov, E*}. 

Sigr. C. MarLL 

Sigr. A. Mascari. 

M. J. Mascart. 

Prof. E Milloaovich. 

Sri Kalinath Miikherji. 

M. A. A. Xijland. 

O. T. Olsen, Esq. 

Sr. F. Com, 

J. A. Parkhnrat, 

Prof. E. C. Pickeni 

Prof. W. U. Pi.:keriiig. 

MiBs K. Plunkct. 

Sigr. A. RafFalli. 

Dr A. A. Rainbaut. 

Herr S. Riefler. 

Dr A. KiKuenbaclu 

?T^, Q. V. SohuipawlU. 



Feb. 1907. 



and of Persons, etc. 



299 



Dr R. Schorr. 

Herr A. Schwassmann. 

Prof. T. J. J. See. 

Prof. H. Seeliger. 

Rev. W. Sidgreaves. 

M. A. Souchon. 

Messrs E. and F. N. Spon. 

G. K Sutcliffe, Esq. 

H. Dennis Taylor, Esq. 

S. D. Townley, Esq. 



M. Ch. Tr^pied. 
Prof. H. H. Turner. 
Sr. V. Ventoaa. 
R. J. Wallace, Esq. 
Major-Gen. J. Waterhonse. 
W. H. Wesley, Esq. 
Prof. Max Wolf. 
Prof. A. Wolfer. 
Subscribers to the 
Huggins Portrait Fund. 



300 



Lxvn. 4. 1 



ADDRESS 



i 



Ddiured b}/ tfte President, Mr William I!. Mate, on pretmtit^ 
Vie Chid Medal of t}U Society to Fro/euor Kmeti WiUiam 
Brovni^ February 8, 1907. 

The Gold Medal of tbo Royal t^tttronomical Society hu ibk 
year boeii awarded to ProfesRor Ernest William Brown (or hit 
"ReeeArches tti the Lunar Theory," and it iR my duty to put 
before you on the present uccaaion the grounds for thia awanl. 
In attempting this, 1 fear it will be impoHsible for me to ds 
adequate justice to the importaDcc of our medaUiat's work. Tb 
work is of so special a cliaracter, atid iT« development has ben 
marked by the introduction of ao many original devices aod 
methods of calditaLion, that an address such an thia is qniti 
unimittid for an uxomiiiatiuu of the duLaiU of the resoarch. All I 
can hope to Ao is to put hefore you the broad foaturee aaJ 
general extent of Profeflsor Brown's work, and to rec(»d the 
success which he has attaineil. 

ProfesKor Brown is the sBveulli astroniimer to whom the OaU 
Modal of the Royal AstroDumical Society lias heou awanled foe 
woik in connection with the Lunar tlif^or}-. His predeceseors were - 
liaron Damoiaeau (1831) for his "Memoir on the Theory of the 
Moon," anii for hif^ Lunar Table!); M. Jean Plana (1840) for bis 
work entitled "Tln-orie du Mouveinant dt* la Lune"; Professor 
P. A. Hansen (i860) for his Lunar Tables; Profesaar J. C. Aduu 
(i366) for bis "Contributiona to the Development of the Lunar 
Theory"; M. Uelannay (1870) for bis "Thoorie de la Liuio"i 
and Dr O. W. Hill (1887) for liis "Researches on the Lasar 
Theory." This is a long li^t of illustrious workers, and with them 
our preaent medallist U well qiialitied to rank. 

In a paper entitled "Theory of the Motion of the Mocn, 
containing a New Calculation nf the Kxpresaiona for tbt 
Co-ordinates for the Moon in Ternis of the Time," published in 
volume liii. of our Atemoirt, our meilallist has stated so cleariy 
the nature of the problem on wtiich he has been engaged that I 
may be permitted to quote from bis introdurtion. He say*:— 
"The formation of numerical expressions deduced oa a consequencr- 
of the Newtonian lawa of motion and gravitation which shall 
represent the position of the Moon at any time may be rough. 
diviilei] into three stages. As a lirst step, we consider each of 
three bodies — the Sun, the Earth, and the Moon — as a sphere 
raasa equal to its acta&\ ma&s, uv^ ArRkx^9,«d In concentric ikjreia of 







Feb. 1907. 



The President's Addresif. 



301 



I 
I 



(Hjaal deriHity, The Earth (or the centre of tuasA of tbe Garth and 

^loun) is supposed ta move round thd Son in a cortAin ideal 
elUptic (irbit, and all disturbances of this orbit and of the Moon 
from any other source than the ideal Sun und Karth are neglected. 
This tirat st^e constitutes nearly the whole of the labour of 
solving the problem of three bodiea as far as the particular 
configuration ul' the Sun- Earth -Moon syatem is concerued. When 
tbia ia Aana, we pro^^eed to the second step, which involves the 
dctermiuation of the clfeota due to the difference between the 
actual acid the ideal motions of the Earth and Sun, to the iufluence 
exorcised by the other bodies of the solar system, and to the 
differHnces betwepn the rcml and ideal arrangements of the majAseit 
of the hollies. The calculutiona so far may, theoratically at least, 
be made without any knowledge of l)ie configuration of the 
system At any given time or times, beyond a goneral idea of the 
order of magnitude of certain of the constants involved. The 
third and final slage consists in a determination by obwrvation of 
the various constants n'hich havt; oTitt-red into the theory and the 
eabdtitution of their valuea, so us to obtain numerical expressions 
for the co-ordinates in terms of the time." 

As we shall see later, it is thu oompletion of the first of these 
stages which hai^ priniitrily been the object of Profemsur Brown's 
put laboui^ ; and ati a result he has, after arduous work extending: 
over the past Gfteeo years, completed the solution ui the problem 
of three bodies for the case of the Sun l^rth-Moon with an 
accuracy very far in excess of that attained by any of his 
predecessor^ in this line of research. 

Our kno\vlLHl>,'e of the motion of the ilooa has accumnlated 
daring long ages; bnt it is, of course, only since the time of 
Newton, or, say. during the past two and a half centuries, that 
the Lunar theory has bod any existence. Our earlier information 
as to irregularities in the Moon's movementa was knowledge 
derived from observations, and it did not include any explauatious 
of the causes to whic-h these irregularities are doe. Before the 
discovery uf gravitation, nil th.it could be done with the motion 
of the Moon was necessarily empirical. But even Nnwton, the 
discoverer of this principle, contented himself with the variation, 
the motions of the jjerigee and node, and the largest inequality of 
the latitude. Analytical expressions giving the position of the 
Moon in »\\&c» were not seriously attempted until the middle of the 
eighteenth century, when three men simultaneously concerned 
themselves with the problem. They were Clairaut, Ii'Alembert, 
and Euler. The lust-named, in 1753 and 1772, produced three 
Lunar theories nearly independent of each oUier, and of the third 
of these I nhall have more to say later. 

Of the six inequalities which affect tli^ ftfoon's posiition by an 
amount capable of being discovered by uakcd-eye obsorvations, viz. 
the effect of solar attractiou in enlarging the Moon's orbit, the 
revolution of the tine of apttidea, the regi'ession of the nodes, the 
erection, the variation, and the annual w^uatitm, onV^ ouft — ^CtoaX \o 



?02 



77m PrtaidetU's Ad<lre«s. 



IJCVIL4. 



vhich the name of **evectiou" was given by Boulliaud in lh« 
Beventeeath c«Qtury^ — was known to the ancieuU. It appean 
have been first noticed by llipparohus, about 1 50 B,c., when b« 
was engaged in endeavouring to jetennine the Moon's distAuoe, bat 
it waa first taken ByHtematically into accouut by Ptolemy, to whooi, 
indeed, its diicuvery has been attributed. 

The vari&tion, which lias a fortnightly period and a zero value at 
syzygies and quadratiiree, does not itirvvt the time of au eclipse, tad 
thus escaped the notice of the Greek astronomers. It appear^ 
however, to have been detected by an Arabian asironomer, Abool 
Wnla, in the tenth century, but was lost sight of until redtsooruW 
by Tycbo Braliu about tlie end of the »ixttH.-mli century. To 
Tycho Brah(^ is also due the detection of the anDual I'quatiuu, 
although he gave it an eironeous vahie. A more correct vaJtie ns 
determined by Horrocks, but its true character appears to have 
been first appreciated by Flamsteed. 

Of smaller perturbations the number is almost endless — wveot; 
such perturliatioiiK are, 1 understand, taken into account tu th« 
calculations of the Moon's longitude made for the Americaa 
Ephemeris, and about half that number in the cotnpatations for 
latitude — but of these the most important, and in many ways the 
most interesting, U4 the secular acceleration of Uia Moon's mean 
motion ; and on this I desire to say a few words. As early u 
1693, Halley, after a consideration of the records of a number of 
ancient eclipses, arrived at the cuncluabu that these records oouU 
only be satisfied by assuming a progressive shortening of the Lmur 
nionth. A long period elapsed before this suspicion ivas confiraed, 
but in 1749 Dunthome contributed to the Royal Society a paper 
discussing ^1 available observations bearing on the su)>ject, and ths 
matter was further investigated by Mayer, Bouvard, and Burg. The 
explanation of the acceleration, however. Ion;; evaded the eflbns 
of the mathematicians, but later the problem was taken up by 
[jiplace, who at length, on November 19, 1787, announced (o 
Acadi^mie des Siciencea his discover}* thut — "The secular equatii 
of the Mmni is due to the action of the Sun on the Satelli 
combined with the secular variation of tho eccentricity of 
terrestrial orbit." 

Laplace's tirst value for this acceleration was ii*'X35 
ceutury : a value subsequently reduced to io''i8. The catise 
this inequality acle on the Moon a^ gravity on a falling body, and 
its effi-ct, therefore, is as the square of the time ; but in catiying 
'the calculations l>ack to the time of the Chaldean ob««.-rTatious, i 
was found necessnry to add a small teriu dfijieiiding no the tin 
cubed. Thus \i t = the number of centuries from the asau 
epoch, the acceleratioti, acconlUig to LnpWe, was equal 
io"-i8i9 /^ + o"-oi8s4f3. 

These deductions of Laplace were verified in 1S20 by two of 
our medallists, Banioiseau and Plana, and also by Carlini, tbeir 
approximations being oarried to a higher order Uian those of 
Laplace. The TaVut d«\nwl Vrj \)vinv>\iita'a was io'*7j, and \t^ 



\ 



yin«^ 

1^1 



Feb. 1907. 



The J'raiidtnl's Addrm. 



303 



Plana io""s8. These valaes were all too large; hot the error was 
uL oucv fortunuti! ami unfortuuatr. It wus fortuuale in bo Ear that 
the values arrived ul fairly Botiuried the discrepancies between the 
recontft of ancient eclipttrr^ and ttie results of modern ohscrvatioos, 
and led to the acceptance of the explanation and Lbe upholding 
of the ^ruvitattnnal theory ; but unfortunate inaxniucli &n this 
doae agreement lad Uie effect of stopping; for the time further 
reaearch. Moreover, when some twenty yeart) later Hati&en took 
Up the rnatt^ir, ho also arrived at a Inr^c value which he anounnced 
in 1842 as ti'*93, reduced in 1S47 to ii"'47. 

Things remained thuH until another of nur medallistti, Professor 
Adnois, look up the problem ; and on June 16, 1853.. '" ^ p^per 
read bcfom the Kojal Society, pointed "lut an ini]ioitaiit error id 
the w«trk of Plana and Damoieteaii, and showed that the corrw:iiot» 
of this error mont niattrially rodiiLed the value of the acceleration. 
TItree years luter, Plana was induced by Adams'H iaveatigtitionv to 
re-eiaiuiiie a pnrtion of his own work; and in April 1856 he 
admitted the imperfection of his theory, and dedncfid a. result 
ai;reeing with Ihut rif Adams. A little later, however, he withdraw 
thi-s admission, and deduced a Talne differing both from that of 
Adaius und hia own original result. 

Adams's investi^^'atioDs led to strong discussions between the 
chief mathematicians of the time, and hit* deductions were not at 
once accepted. Thej were oppoaied by de Pont^oulant, and io 
1857 Ilausen piibtisheil his T(ibl«i$ ifs la Lune, in which the 
value adopted for the secular accak^ratlon was I3"'i8. lu 1859, 
howevt^r, the investi^tation of this part of the Lun«r theory was 
taken up by Delaunay, another of our meilallists. Adams had 
■hown that in a certain series in m\ m*, etc. (thi:* term m* being 
absent) the term m^ hatt been wrongly calculated, and that as a 
result the numerical value nf the secular acceleration mast be 
approximately halved. Delaunay, carrying his calculatii^ns to m*, 
obtained exactly the same result a^ Adams ; a result which he 
announced in January 1859. This induced Adams to publish the 
value he had alraady obtained, using terms involving m", m^, and 
m', the result being to give the coefficient uf secular acceleration 
the value 5"'7, a reijult suh»c<iuently reduced to $ '^^- Again 
Delaunay touk up the matter, and on April 3^, 1859, he com- 
municated to the Acaihhnie ties ficittucps tbo result of his investiga- 
tions, cunfirminH Adams's new term : »nd, by carrying the approxi- 
mations to the 8th onler, deducing the value 6"'i i. 

Into the further stages of this important controvei-sy it is 
tinneoesBary to enter, hut ultimately the results ui Adams were 
Accepted. The acceptance of his value, or of a close approxiniation 
to it^ leaves the remaining' discrepsncy betwrwn theory and the 
ri'Aulta of oKsen-ation to be explained by nome other cause or 
causes; a work with which Mr CuwelL is at present prominently 
identified. 

tThe next important step to be noticed in the development of 



I 



304 



The riv&Umft Address. 



Lxvn. 



1 




The fottures of that vork veve most adtnirably daatt vitb id tiit 
AJdroM delivered by Dr GlaJuher on the occasion o{ the Gold M«iUI 
bfliiig Bvarded to Dr Hilt in 1 887, and it would be quiU; impuMibU 
to iammiuw} ihcm beru. It need only be said that — foanded to 
0oua extent oa a suggvstion cuntaiiied in the \M\teT (to wfateli 
reference has been already made) pablished by Ruler in 17731 
aamely, that of employing moving rectan:t;ular ronirdiRmta^ 
ombodying entirely uovel uiethoda of dcvelupineut, of Um bij 
inlvreat from the point of view of both the pure ott' 
and the adtrononier — Ilill'i work opened out a new ngion 
theoretical research, at the name time intnxluciog great aim 
tions in tnethods of practical calculation. 

Muny other dittiDguished names will 110 doubt cKcur ta ytn 
as»tKiate><l with tlie deTelopraent of the Lunar theory, such •■ 
Airy, Donkin, Cayley, and Newcorab, but time will not permit 
my oatering into the detaiU of their work 00 the pr«Mnt occaaioo. 
I moat («aa ou to consider xome of the aalient features which baT« 
marked the dovelopmeat uf tlic Lunar theory ; uud in doing thia 
dtjsire to expivKs my iiulebtedneeM to Dr (i. W. Ilitl for mu< 
Taliuble information r«)lating to this branch of toy subject, which 
be baa moat kindly placoil at my tliapoflal. 

Thu iucdSBdnt call for gruater preoiHioD 10 dealing with t) 
motions of the Moon has led to frequent npetittona of troatnii^nt 
this subject, so that wa are now in {lusMMiou of tou nr eleTea 
Lunar tbeoriea^ each profeasing to go over the whole ground. Thft 
advance in prorision is obvious from the fact that while Koler 
cooteuted hiiusdf with about thirty periodic torma in the longitude, 
Profosaor Brown haa neurly four hundred. Aa would be expected, 
each investigator has adopted such ^ mi'thod as. in his judgment, 
would lead most promptl)' to the deeired eno*. TboM! judgmenLa, 
however, from the u«ce»ity of the oue, cau be ou';,' t>"<bal)le oun- 
oluaioQp. Thus thu Luuar thL'oriea we have now before La esliilitt 
much variety. 

Ilie broadest division of these theories which can he maiie it 
into tlie two olaaeea of litsrai and ummtricaJ. Kor the first, all the 
qtuntitieaon which the nwult tlupemlii are re|u-es'-nt«d by al^bmie 
aymliols; whiln in the second, the invnstigaton have attempted lo 
fhorton their labour by introducing at the oulaet the numMWftl 
Tallies of as many of the quantities u the nature of the prublam 
admitted. The much gtvaler labour involved in the etabaratioB of 
a titertii Lunar theory has brought tt about that of our ten or 
eleven treatments uf this oulijuct, only three an litntU, viz. th<i«e 
of Pluia, de I'uuliWitmUtit. snd Di^launay. But thia method nf trr«t- 
menl is much more satisfactory to the matheroatteal mind, while it 
alao poMMHaea obvious attviintage* over the numerical mt>th<Ml, In 
the oarlior days of the Irealiut-nt of our problem it seems to hav« 
bwn Uiuogiit nearly imprsctiL-ablo to ailnpt tht< literal method, 
■ad to Plana must l>e acomled the merit of hsvin>{ f)r«t elabnrat»l 
aocb a theory. Prufeasor Brown's theory is partially UtfTal aiid 
partially numerical. Of tlm five parameten involved in the pre- 



BuV 



Feb. 1907. 



77ie Pitsident's Address. 



305 



r 



I 



aentation of the Lunar ctMirdinatea, four are left iiuleterminate, 
itiid it is only tho ratio i>f tbe month to the year that receives a 
definite: numerical value from the begituiing. 

We next hnre to note other varieties of treatment. In the 
surlier period it was a favounte mtithnd to atlopt the tru>> longitude 
«f the Mood an the indepeiideat variable; th'il in, in the first 
in«tanc«, the iucjiu longitude, iHtitude, aiid reciprocal of the radiue 
Were determined in ttsrnis of thu true longititde, and there remained 
the taiik of inverting theae fornmlas, Thin wai; the method of all 
the early elaborations, except tlie Iiut theory of Eiiler, to which 
reference had already been made. On many ground^ it could, 
no doubt, be defended ; but it soi-mB that it was Poiwon who Hrst 
threw diiicredit on it. His pupil, de i'ont^coulant, adopted the 
time as tbe independent variable, and so also did Hansen. 

I must now din^ct attention to tbe most prominent of tbe 
l^uliarities which mark our modallittt'tf eluburaiion of the 
problem. This may be -stated as the complete milisatirm of the 
circunistancfl that, Batting a^iiie the rate* of motion of the elementB 
of the ar^imientH of tbe p«ri(*dic terms, the analytical exjiresHionti 
of the three co-ordinates are cajiable of being acparated intn 
portiims, each factored by certain i>ower*t and proiluctfl of the 
four parameters which Pmfftasor Bmwn has left indeterminate in 
hia formulas. TheHe factors have been termed *' charactcrit^tica." 
The advantage of considering thcJie portluuii in, tbut each can be 
determined independently of the adjacent, so to apeak, portions ; 
while the treatment depAuds on the portions nf lower degrees, 
which have been precedently treated. The credit of having in- 
troduced thix notion must be given to Euler, who employed it in 
his last treatment of the problem, publit(h'--d in 1772. 

Very closi-ly connected with the foregoing principle is the 
device of makinji the Moon'a mean longitude disappear from the 
equations employed in the treatment. Intttead of UHingco-orditiateit 
referre<^l to fixed axes, there are oujjdoyed tliosw referred to two 
axes in the plane of th4> ecliptic having a velocity of rotation 
eqoal to the motion of the Moon's mean longitude. Thie con- 
trivance IB aUo due to Ktiler. 

From the use of thefts two principlen r(wult«i a distinguiabing 
mark io the treatment. Every treatment muat begin with a stage 
called tliat of the first approxinmtion, from which, by dcgi-cee, 
a maperior precision is attained. All the Lunar theories mentioned, 
except the two particularly dnacrihed, Atart from the Keplerian 
ellipse, ur this moilified by moving lines of a]Mide« and no'Jes, as 
a first approximation. But in the lost theory of P^ulur, and that 
of Professor Urown, tbe Hntt nppn>ximatiou is the variational 
curve, already somewhat roughly derive-! by Newten in the 
Principia. It is the fashion now to call this a {>eri(xlic solution, 
ae the inequalities of motion go through all their vurieties in a 
hination ; but we may arrive at a notion of the mutter more simply 
in the following manner :~The motion of the Moo\^ Vaxy«i\^ ^i*:^ 
pends on th« constant called the eccentrVnit^, atvA ^\\ft wswiWAA 



3o6 



The President's Atldreis. 



tgbt uk^l 

? that ill n 



might have the value tero; in like manner, the motion mtgbt 
place in the ecliptic ; the solar eccentricity might h« sero : 
in fine, the Sun might ha t^iippiKteJ at such u diittHnce that 
actiuii in didtutbiiig tbu relative position of the Mouu lui^bt ht 
regarded ae always parallel co its action on liie Karth. Let 
theM four poeaibilitieft be fulfilled ; the result is a greatly simpU 
set of difTereutinl equations, easy of solution, aJthough methods 
approximation muHt «iCill l>e employed. 

Having obtained thid ijohttiou, we are prepared to advancv 
turllmr. Lvt it bi! granted that the four mealioiied canstAuto, 
inntend of having zoro value, have values bo amall that tlieif 
iu|uart^s and pruducU may be neglected. This suppositiuu givM 
rise to a set of equations denominated by M. Potucar6 aa " eqoatinni 
to vBiiotion." They are of the clatw known a^ "linear," and 
generally more easy to integrate than tfaoM called ** nuo-li&Mr.' 
Their uioMt important qtiality is their being, ivith the exoeptioQ of 
the known parts, the aaine in all the ntuges of the appro xitnalkm. 
It thus resultti that a ronsidcnible portion of the calculntions made 
for the second t^boge of the approximations is Htill available far 
all fullowing. 

It may be stated that the series which satisfy the differentiil 
equation)) of a Lunar motion l)e]on^' lo the clans uow known ti 
Lindstedt »t-iios, or those resulting from the addition of terma,aarli 
the produrt or two factora, uth'- toeing a constant, tho other « siti« 
or a coi^ine of an angular argumeut, the latter being equivalent to 
the sum of positive or negative integral multiples of a definite 
number of elementary arguments. In the restricted form of Uis 
Lunar theory treated by Professor Brown the definite Duoibor h 
four. 

In the elaboration of the integration it is not only nAce.<«ajy to 
(leteimine th« constant factors of the series, but the ilerivation oi 
Uie motion of the elementary arguments. The lattor have ramilar 
forms with the coefficients, and, like them, cannot be detenoineJ 
at one step; we tniist be content to dcrivt the successivQ portiou 
in their turn. In the Lunar theory the matter is eomewbit 
alleviated ))j the circumstance that the motion of two of t-he four 
elementary Brgumeots may be regarded 04 known at the outset 
is necessary ordy to dcrivi- the rates of motion of the m- 
anomaly, and the mean argument of the latitude. At parti 
stages it beromef^ necexHary to notice thai the previoiifilv-o»f«^ 
motion of one or the ikther of the arguments needs corrtMtion by 
the adililiou of a new set of terms. 

Wtien thu Liudsdtedt stories are substituted in the equations te 
variation, the result is a group nf lint-ar algebraical equations in 
number precisely sntticient to determine the coefficients, or Ifaa 
corrections to coellicients, as wi-ll iis tliu corrections to the motioM 
of the arguments, if there be any. For solving the abor^ 
mentioned group of equations the most fensiblo mothod of treat>i 
ment to adopt is still that of fiucoeasive approximations. The mi 
imjKtrtant quantity to be noticeil in this solution is ihedeterniina 



* 



whit 
foot ^ 

meslH 
IcniaM 

-n«J^ 



4 



Feb. 1907. 



The Fresidtnl's Address. 



307 



of tlie equations. Not anfrequently (bU quantity is much smaller 
timii tliu coufficleuta from which it is derived. When this is 
the case the coetHcient'=i iuvoWed must be computed to a corre- 
spondingly greater degree of exactitude. In two or three cases the 
mattcT is 80 pressing that three more decimals must be added fro 
the %'alues of tho quantities iuvulved. This iii the mocit troublesouie 
oirciiuiAtuncu utt4.-udiDg the elaboration of a Lunar theory, and 
▼oriution uf nit^lhod does nothi^^ towards thv removal <jf it. It is 
very vcxiriy for the investigator to find that he must return on his 
£t6ps, and pnsli certain <|uantitieH to a higher itigrc^ of precision. 
Tlii^ matter is so complicated that it is impossible to prescribe 
a priori tmIvh for prucedure. Detuunay iu his Lunar tlurur)' has 
noted, al the foot of the page, nil tlit* pliu^es where such a 
raodiHwition of proceiw was nHcesKary. 

8uch, in brief, is an outUue of the method of elaborating a 
Lunar theory t<Miay. In bis paper, to wkicli n.'ferunce has alrendy 
been mtide, published in vol. liii. of our Metnotrs, our medallist 
stated tliat he had tht^n (1897} been engaged for six years in 
attempting to develop the ideas contained in Hill's *' Kesearches 
in the Lunar Tliixiry," by calculating Uie coe{1icieuL<4 of terms with 
curtain dufiuile characteristics, to which I have ahruady alluded ; 
and he detines the " characteristic " of any part of a coe&icient aa 
being that part of its expression which consiata of powers and 
products of the eccentricities, the inclination, and the ratio of the 
mean parallaxes. He goes on to say : ** Dr Hill hud abtaiued these 
which hud the characteristic unity, that is, wlii..-h were functions of 
the mean motions of the Sun and Moon only, and also that part of 
the motion of the perigee which vtag a function of the same 
quantities ; Adamn hud dune the same thing for the motion of the 
node. It romniuod, therefore, to obtain the general equations, t*) 
put them into foruis suitable for calcuhition, and to show how tlia 
other parts of the motions of the perigee and node might be 
obtained." 

T nnist now notice the degree of advance in our knowledge of 
the Lunar motions, attained through the labours of Piolessor 
Itrowii. When Professor Xewcomb mode his com|>ariaoo of 
Hansen and Delaunay, we were in doubt as to the vabio of 6ome 
of the coefficients in longitude to the extent of half a second of 
arc at least ; aiao the motions of the perigee and node were 
uiicerLain to correspondingly larger quantities. On the other hand, 
the decree of accuracy aimed at by our medallist has been such that 
there t^hould 1w included the coefliciencs of all jierirtdic terms in 
longitude, latitude, .ind parallax which are greater than o''Oi of 
arc, and that the results should be correct 1:0 this amoimt. That 
he has been able to carry out snoh a programme is assuredly a 
matter demanding our heartiest congratulations ; in fact, with such 
a notable advance one is almost inclined to say that there is nothiD|i 
left to be desired ; however, this phrase has beeu so often upset 11 
the post that it would bt^ unsafe to employ it, 

A natural question here arises : " What will be the effect > 



308 



TKi PresideiU's Addrets. 



LXVU. 



ursV 




Prof«»»or BrofTn's reaearcbes on the accunicy of Lanar tal 
based upuii tlieml" Tbis is a question of great interest and 
importance, but in the prei^ent stat« of our knowledge it is od« 
to whioh it IB difficult to ^ve a definite answer. It luut, howrvcr, 
been my pririlego to receive mi expression of opinion fruni 
G. W. Hill, who speaks with the Iiighest authority, and thi 
opiaioD I may be permitted to quote. He says : " Much as 
(fitly welcoiiiP the n.'»ult8 of Profexsor Brown's dovoted labour%1 

should b« unwarranted in assuming that their employment 
the Lnnur tahleM would g;ive rise to a roarkcul imprnTemeaft^ 
in the rapreaentatton of observatioua. A slight one indeed mi^li^| 
be expectivl ; but it has boon evident for some lime that th«^ 
Moon deviated from its oalculateil orbit more bscaase it ia eubjsct 
to irregular forcei*, which we have; not yet the means of eatimattni 
titan because ibo tables are affected by slight dafect« in 
mathematical treatment of the furces which are already recognic 
Thin circumstanci* in no sense diminishes the credit due to 
fesAor Bmwn'fl work." This is a very weighty expresaioD 
opinion, and it indicates that there is yet ample work to be d<. 
by inveatigatorti of Lunar motions. I should adi] that MieL 
research has been most materially aided by the im(M>rtaDt wurk 
of our uiedftlliflt, wh-i, by giving accurate values to the known 
perturbatioDs, has defined more clearly the furtber irr^:ulM'ttti 
of which the explanation has vut to be ascertained. 

I have perhu]>!i, in this address, dwelt at twmewhat 
length on certain matters of a more or tees historical cfai 
but my exciine is that thfi facts I hate stated may serve to 
emphasise the difficulty and the onerous nature of the work in 
which our medallist ha.4 been engaged. Tliat he has succeeded 
in makiiii^' ^reat advances in a field of research which has received 
the dee]M»t attention from the leading mathematicians of the 
world for the past century or more is in itself u must eloquent 
testimony to his powers. It must be borne in mind that iu a 
problem of this character, the scdution of which dependn upon to 
many divorae terms, the investigator has not only to acquire soch 
knowled};e of the various terms as will enable hitn t/O dtseard 
thoHt) uf which the inlluenx^f- is unimportant, but he has also, in 
the cose of those rtttained, to devii-e such methods of treating 
them as will enable them to be practically dealt with in a reasoa- 
able period. In both thesi> respects our medallist has 
admirable results. Knrly in his work of calculating iDe4|i _ 
whose chnmcteristics are the first, second, and third powers 
the ratio of tlie mean parallaxes of the Sun and Moon, and 
same jKJwerji (►f the eccentricity of the Moon, Brown found that 
thf) forms of equations then available left much to be detsilnd, 
and were apt to load to errors in the practical calculntioDs ; luij 
in a paper entitled *' Investigations in the Lunar Theory " 
Irihuted to the Arne^ruan J<mmal of MathematieM, vol. 
he slioweil how these dillS^culties cuuld be avoided and the )< 
of computation dimiuwVicA. 



Known 
iarttta^H 

andtfl 

iraeM^ 





Feb. 1907. 



The President's Address. 



309 



The thoronghly practical cliaracter of Brown's method o( 
work * is most striking. Speaking uf the value of ICuler*!! 
sugRealions, he has hiuiaelf said: — "The working value of ti 
method of trciitment i» not really tested by the cliweness with 
whicti the first or K»coiid approximation will make the further 
approximations coiivcrge quickly lo the desired de^^rco uf ac- 
curacy ; the real text is, pffriiapa, the ema with which the linal 
Bpproximatiou can be obtained. Here we have the essential 
difference between the prosont method and nil other mothode. 
Tlie approximations of the latter proceed along powers of 
the diptiirhing force. Ruler's idea was to approximate along 
powers of the other small conatanta present. This gives a 
most rapid convergence, and a degree of certainty in knowing 
the limits of error of the Snal reenlt^ which no other method 
approaches." 

In Or letter which I have received from Professor Brown he 
modestly elates tlmt the only ]>ortionft of his woi-k prasenting real 
difficulties were those arising from the direct and (Wtrei^ actions 
of the planets, On appmarhing these problems be found the 
subject in a somewhat chaotic state^ and it was neceasary to clear 
the ground and get the theory into good shape. In doing this, 
the first requirement was to bt* able to compute the derivatives of 
the Moon's co-ordinates with respect to w = the Moon's mean 
motion. But in our medallist's theory the numerical value of n 
had been snbstituteil, so that the derivatives could not be calcn- 
latwd directly from it, Delaunay's literal theury might have been 
used for the purpose, but, owinj; to slow convergence, Professor 
Brown ilid not con»^ider it accurate enough. Under these circtim- 
Btauce.'* he succeeded in finding » method for getting thfse derivattveR 
accurately from hi^ Lboory, in spite of tbu fact that the numerical 
Tftlua of n had been substituted. The idea which led up to this 

* T1k> rocfinln uf irtir mwUllwlV wwrk 1iji»b benn Ur^nly «..utitain<^ iii 
papers eotitrLbut«d to our Society. In Msy ito7 Prornssor Brown Hut in 
Fitrt I., I'h&iilem i 104, nfthe p*(')«r entitlerl "Tri«ory nf iho Holion of the 
Sloon, ontaiiiiOK n Jinv Caloufation at Ihe ExpresaiDnii fur llie Co-onllnaus 
of the Haoti in Tsrtiia of the Time," from which I hare already quoted ; ari<l 
thi^ wa-i fnllowed, in February 1S99, by Part 11. ; in May 1900, by Part 
III. ; and in J&DUary 1905, by the eoaclusioii. Part IV. [t'srta I. nnd II, 
of PrnfiMor Brown's )»]>rr ant conUiiiiwJ in vol. Hii,, Part III. in vol. lir,, 
ami Fa,rt IV. iu vol. Irii. of the Manoin uf th*> R.A.S.] B«8i<lfv tins, b« 
eontriliutw] a number rif rapeia wbiflh hdvc appeareii in nur Mtmthtff Xittiets, 
namely, " On the Mean Mocions of Lunar Pongeo and Xode," and " Oa the 
Tbaoretical Valaea of The S«oiiIar Ac«elerfttioas in the Lunar Throryt" 
abiitracta of which antteareil in March 1S97 : a {■aper eotJtUd "Not« ( 
the Mean Motions of Lnnar Prrignr and Ifodp," ptibliehed Jiin» 1897 ? 
"On tbo VeriScatinn of the Ni-wU>nian Law," which a[ii>car«<] May 
two li«p«ra eutitlMl n;it{)«ctiTrly " Od the Degree of Aocuracy of tV 
Lunar Thoory and on tht Kinul VnUiea of the Moan Uotiooa of the 
anJ Kode,'' and on "The Parallactic lueqaality and thn SoUr Pai 
iinblisheil April 1904; one "On the Completion of iIir Sohition 
Main Problem in the Kew Lanar Theory," puhliabed Deoeinbtr ti 
one "On the Pinal VaJun of the CoeBioietitii in tlie Itew LatkU 
ctnitained in JtfmtM/y li'atirts for Jannary 190^ 



310 



The FiesidetWa Addnsa. 



LXVU,4. 



method was first aUted in a p(L[)«r* contribute-l to thu CAmbridga 
PbilositpIiictU TrHiLMctiout in 1S99: aiid ihu luuthud iUMlf, nbicb 
U believvd to bu quite new, wa-t dealt with in a i>aper t contribttted 
ti the American MatheniHtical S<)>nety in Potivuary 1903. Sinea 
then tbn calculattoiut have been performed, but ■» not jtt 
published. 

The ctlcuhitioii of the indirect inetjualitieK ^ave ooo»idenbU 
trouble, but Profeasor Bi-uwii vriiti abU- ultimately to abow in 
pft]>er * contributed to the American Mathematical Society 
February 1905 that it was not m^-fe^ATy to ealcal&te the pertur 
tiuns of the Karth by the planvbt in order to get the renulti 
effect on the Mood, but that it was possible to go straight 10 
disturbiuj; function of the Karth by the planet. The ciilculations 
the direct incqunlities lirere completed la^t autumn, and Profi 
Itrown hope-s t.o publish tbem during the ensuing summer. 

The precautions taken by our medallist to secure aocurairy 
tbfl final resulte iisve been most refined. In accordmice with I 
original prOKramme^ erery coefficient iu longitude, latitude, s 
[tarallax, which is so great as one-hundredth of a 8eiu>ni1 of 
been computed, and Is regarded as accurate to at least this 
the rasuttd being really ubUiined tu une-thouKaudth of a 
To avoid the occurrenco of errors of oomputation, eqaattuns 
vorificatiou have he<ui computet! at overy Rtap of the work, ev 
page of the manuscript having, on the average, not leas than t 
teH equations computed. 1 am indebted to Mr Cowelt for 
remark that our medalUst is the firtft Lunar t]iei>riat to use in< 
pendent o^piaiions of writicution, thus creating a highor decree 
L'ontideiico in bis results tlian could «ver come from mere dupli 
calculation. U was bis d«'vice to form the equation for a small 
variation of this solution of Hilt's etjuations. Says Mr Cowell : — 
"The uumeriral applicattou of this device was rendered iMieeiblc 
by cakulating series ftir various complicated fractions of the 00- 
ordinates in Hill's variiitioa curve. Tbo utility of the plan ia 
obvious as soon as it is got into working onler, anil its coboeptioa 
implies rare insight on the part of our mcdalliAt. It lios at tha 
root of his success in obtaining more accurate results, with I 
labour than his predecesaore. He has also obtainel theorems 
which th" higher parts of the motion of the perigee and the u 
may be c^toulated in advance of the oorrespouding group 
periodic terms." 

For the motioos of the perigee a&d node, the final values 
obtained, and a cooiparison of these values with the resulta 



ina 

1 

Hues 



* "On the Solution at s P«ir oT Simultaneous Linear Diffareniial 
lioiitt wliit^h Mvur ut tbu I.uiiiir Tll«ory," CatttAHif^ nUMoj^itai 
adiofju, vol. XTiiL 

t **0u tlid Formation of the Derivttivcs of the Lnnitr Co-ordinatrc tritt 
Bsspvct to Uie £l4!iiii>iiU," Traiuarliom of the Atueriean MaUuyivUicai . 
vol. ir. 

t "On a Q«nerml Method for Trmtiug TrsjuuiittMl MntionR, 1 
Apf'Iioation to Indirect Petturbalinns," 7VimM(4t«n« (/ th* vtirwn'stKi 
matiatt Socitiy, veL vi. 





I 



Feb. 1907. 



Th€ Prmdetii*s Address. 



3H 



observations, were given iu ihe paper publiabed in the number of 
the MmUhly Notices for April 1904,* to which reforeiion haa 
ulreaily 1>ecu made. Iti ^jiving these valueit our mediLll)?t pointed 
uut that there wa? one constant of which the obtmrveU value was 
BO far doahtful as to atfect thu reaults by as much as the tenth of 
a fiucond, ihio coiistaDt beinn the elliptiijty of the I'larth. As there 
apptAred to be two uuiupetiug valuer for this ccneUint, namely, 
Ywt-ii ^^^ tbV .!> ^etwt^L■'I whicli no definite choice could I>e made, 
Prufeseor Brown decider! to c:alnitltkt*i the results for tlie two 
value«- Tb« final rpsuhs, with the portiona of which they are 
made up, are given in the subjoined table : — 



Finat Mtan Fabut <if Uu Annual Mtan Atotions 0/ th* fimi^ei tmd Kodg. 

Perigw. 



/■Oh«i*. I. 

,1 



SoUr 

Action 






Tenni ia N<>, 3 
Tijnns in No. 3 
PlrniRtAry direct 
Plauctary iiiilirvot 



+ 148 %M9t 
+ 15617 



Koda. 

-69 287*90 

616109 

4- 360-59 

2546 



2'Z4 

■04 
673 
I 51 

-99 

i-6i 

TO ±'04 

70 

•01 



3*661 
•20 J 



±^ 



t*ll 

170 

■05 
■57 

■oS 

■00±'0Z 
"20 

•ot 

1-43 
■06 



\ m 



±■03 



Figtiro of Eftfth («) 
Kpuro of Earth (fl) 


+ 6'S7 
+ 6-41 


6-.S 
6*00 


CaleaUlot sum {a) 
Calculaled anm iff) 


+ 146 4J5'36±'I0 
+ 146 435'io^'io 


-69 67g'38±'05 
-69 fi79-23±-05 


OWtved 


+ 146 435 '^3 


- 69 67945 ^ 



C-O(o) + oxi4±*io + ooSios 

C-0(3) - o'lai'io + oaji-o 

A'o(«.— The " Figure of Earth " valnee " (a) " correspond 

ellipticttr of ,andtbo8e"(^)" toanellipticityof 

* A kltsht vorrectioo to lliv vahieii tLi-rv ifiwD will be found fr 
Notira, vcT. Ixv. p. 276. Thin correoCloB has been utaile in Uw 
uow givcD. 



A 



312 



7*A< President's Address. 



Lxra 



For tliu llHHjretimI jiecuhir uccalenitiona the values fiaalty orrii 
at hy out mviifiliist (lu given iu liIs ptiper published in Mont} 
Notice* for March 1897) are as follows:— 



Thmrnti^ Value* of lite Se<niiar Aeeeieraiion per Cmttur*/. 



The Menn Motion 
TliB I'erigee 
Th« Nmie . 



+ 5-91 ±0-02 

+ 6'56 ± o-oa 



In devising ilu> iletail:^ of hie re»tmi-oh, uur meHallidt arnmi 
the work ko thtkt cunntrlurable propc^rttonR could lie done 
cumputor^ ; but, its u matter of fact^ only odi; — Mr Ira L. Sterner, 
Haverford Collcf^e, of vrltuee ability aud accuracy Professor Brawi 
speaks ill Uic liigbent terms — lias liecn so oiiiploytxl. It may 
interesting; tn quote Imrft Homfl details given hy our m'-daUist an ttf 
the lime aud labour expended un the work. K« states : " Kruu 
1890 ti> 1S95 certain cUih^'S of )rie'4UiLliti(?.s were «aIinilaLed, hi 
the work was only bej,'un on a sy»tL'iuatic plau, which involved 
f^e»h (Mimpututiori uf all ineiiU'ilitios previoutily fouad, at tli| 
bBginuinj; of 1895. Mr Sterner bt>gan wnrk for me in 
autumn of 1897, and tiiiislitsd it in the spring of T904. thou^'l 
ueith'^r of its was by uuy mcau» vcjhtiauoiisly <^)i);B^'jd iu calcnlatii 
during that period. Ue spent tm it— according to a curufully-ke[ 
recoixl — nearly thi«t» thon^ami hours, aud I estimate my aharo 
sam*-- Hve or six thousand h(}iirs, so that the calculations ha\ 
probably occupiGil altop(!tlier al>(>uc eight or nine thou»aiid bom 
There wore iilKiut 13,000 multiplicutiuiui of suriea umdt% t-imtainii 
some 400.000 se^iarati; prcxim^ts; the whole of the work 
the writing of between some four or five miLlions of digits ri 
and milium. Hi;:;iiB," 

Professor Hrown has, as I have statsd, completed hia solutioa 
of the problem of three bodies for the case of the Sun-lCiirth-Mt» 
and hns iicliieved uu accuracy very fur id excess of ibat of any 
bin prffdec^sors ; while he has done ibis by metbo^Is inTotTtni 
striking elefjance and originality, and nlinwing ){reat powers 
resource. He has, however, by no means Einished his labonra. 
he hitnaelf |)oitit«d out, in annuunciug the completion of the mt 
problem, much still remaiDed to he done bofaro it was advisable 
procooil to the construction of tabtcs. On this work our luedallii 
is now engagiKl, and we may rest assured that he will continue 
bring to bear upon it that eneri.'y and power of organised inquii 
which have enabled him already to secure such brilliant result 
Wo may, I think, further hope that in the present award lie may 
find some encoui-agement in his labours. 

1 ronch regret that Professor Brown is not with us thia Qveotng 
to receive tha medal personally, but a combination of circuni- 
^t«nces — amongst them the serious illness of a relative^-bw 
/«n(ldred it imposaii^iU lot \i\mV> ctc«*x.\\ft Atlantic at the preient 




Feb. 1907. 



The President's Address. 



313 



tima. This being so, 1 havH Ikei^n in comrauuication with Sir 
Edward Crey, H.M. Secretary uf State for Foreign Anuir», aud 
I am gliid U> say that liu has Iciudly urnuif^'eJ for the medal to be 
forwarded in Ibe Foreign Office bag to Uis Majesty's C'harg6 
d'Atfaires at Washington, by whom it will in due course be 
transmitted to Professor Itrown, 

T will now sfik Mr Lewin to receive ^e mt^ilal on Professor 
Brown's behalf, aitd to traiixmit it witli our most sincero liofw that 
he timy loEig be spared in full heallli and streuglh to carry out 
ibti important rcsearcbc» to wliivh he has duvoU^d bimsolf. 

Before |>a£mng to otiier huHinetui, there is another matter 
connected witli our medallist on which I should like to siiy a 
few words. I have not alludi^d to it in my addreas, bvcaufio it 
\\siA nothing to do with the award of the meilal, but it will, 1 
think, he of interest to the Fellows gRnurully. As many present 
are aware, Professor Brown is an Ktiglishman who has l>een ]on>( 
resident in America, and who hoH for the ya^it sixtf«ii years beon 
oonnfcte-i with Ua^crford College. That associntiuji will, hnwever, 
be broken in tlio eiiKuiii^ Humuutr, and next autumn Profe&Kir 
Brown proceeds to Vale L'niversity. It is exceedingly gratifying 
U> know that bis work on the Lunar thc-ory, which be ha» been 
abla to carry on at Haverford under on-et favourable conditiona, 
will nnt be inturruptiid by this change. Uy a letter received from 
I'rofes^or Brown, I learn that not only have tba Vale auiborilies 
recognised the imporltince of his work by arranging special facilities 
for its contiuuuuce, but they have alsu most gcuuruu^ly uuilcrta.kcn 
to provide the funds required for both the pn-paiation and ihe 
publication of the Lunar Tables which will form the natural 
outcouie of our roedalliat's labuurs. 



314 Mectwn of Officers and GouncU. txvii. 4. 



The Meeting then proceeded to the election of the Officers and 
Council for the ensuing year, when the foUowing Fellows were 
elected : — 

President, 
H. F. Newall, Esq., M.A., F.R.S. 

Viee-Preddentn. 

Sir W. H. M. Christib, K.C.B., M.A., D.Sc., F.R.S., 

Astroniimer Royal. 
Sir David Gill, K.C.B., LL.U., D.Sc, F.R.S. 
Major P. A. MacMahok, D.Sc, F.R.S, 
W. H. Maw, Eaq. 

Treaaurtr. 
Major E. H. Hills, C.M.G. 

Secretaries. 

Thouas Lbwib, Esq. 

S. A. Saundbr, Esq., M.A. 

F(rrei[pi Secretary. 
Sir William Huggiss, K.C.H., O.M., LL.D., D.C.L., F.RS. 

Council. 

Sir R. S. Ball, M.A., LL.D., F.R.S. , Lowndean Professor 

of Astronomy and Geometry, Cambridge. 
Bryan* Cookson, Esq., M.A, 
V. H. CowELL, Ksq., M.A., F.R.S. 
A. C. D. Cr'immelin, Esq., B.A. 
F. W. Dyson, Esq., M..V., F.R.S., Astronomer Royal for 

Scotland. 
Alfred Fowlki^ K.sq., Assi.staiit Professor of Physics, South 

Ken.singtoii. 
J. W. L. Glaishkh, E-<q., M.A., Sc.D., F.R.S, 
J. A. Hakdcastle, Esq. 
A. R. HiNKs, Esq., M.A. 
E. H. Knobel, Esq. 

E. J. Si'ITTA, Esq. 

H. H. Turner, lisq., D.Sc, F.R.S., Savilian Professor of 
Astronomy, Oxiovd. 




Edvard OeorKe Bloomfield Barlr>v, Ditton Lodge, Stonnrood 

Avenue, Buurtieiiiuutli ; 
Lieut, l". U. Cwpcr, R.N.B., H.M.S. "Ocean," 131 Solium 

Cfiiirt, Cfiiswick, W. ; and 
^:•Iw.lrd l^.wer, R.S.A., F.G.S., 16 Southwell Gardeni, S.W.. 

and Wftership, Nevrbury, Berks, 

were balluted for and duly etfcted Fellowi of the Society. 



One hundred and ciglit presents were aunouoced as baviag be&ii 
recvivud since the la«t mooting, iai;lu'liti}{, umungst otliiTs: — 

Carl Friedricii Gauas Werko, Band vii. {preseoted by Prof. M. 
Breodel) 1 Report nC the Italian Commii^ion on Obeerrations of 
the total wlar Eclipsit of 1905 ttl ALala Chirert, Spain (preitented 
by the CaUnk Observatory) ; J. A. C. OudeiuanBi, Mutual Occulta- 
Lioos und Ecliptsea of the 8alellitc« uf Jupiter (|irtniente<l by Prof. 
Nijland) ; Prague Observatory, Aitrouomiache Beobachtungen. 
1892-99, nebiit Zeiirhiiuagen tmd Studien der jMondoberflache, * ' 
L. Weinek (presflnted by the 01>8en'atory) ; Miillor und K' 
Fhotonmtri»clii! Durchmusterung, GcQeralbitalgg (preaeutad 
Potxdaui Oli^Tvatory). 

Aairographic Charl of the huavp.m ; 40 cluirts prv 
the lUiyal Observatory, Greenwiub, ami 30 charts b; 
Fernando Ohaervatorv. 





3t6 S'ToJ. H. H. Turner, BaxendeWs 



BajceudclVr ObtertatiorM of L^ Geminorum. Edited 
H. U. Turner, D.-Sc, F.ltS., Savilian Frofeti$or. 



1. These ubserviitiuns art) published ai uuc« fur tb« r«uoo 
iiieiitiuutid on p. 119 of this vulauio, viz.: — the Uoivenitj o( 
Utrecht has "•ffered a prire (oji«n t»i Duttih aslrunotnera) for ■ 
dissert at in I] on this VatriaMe, atid therv havi! bceu i-eqiiest» mode 
for origiimi observatioim. 

Mr Jortftph Uaxendell hoK novr piit intit my hmida ibe M 
observatious made by hU father, which go back to iSj6. Inqoiry 
having )iecii lamle as to lliLs particular star, it wa» •.•lli-itvd tliai 
tbetK') valuoble olwmrvutions of variables were for the must pari 
ledgered, but remaineil in the original uhservaLioii t>«>uks. 
theae there ara— 

(a) Thrcf! foolscap yulutue», 1836-4S, 1848-36, and 1856-60^ 

(h) Seven BQiall nou-buoks, 1861 -77, 

(c) A ()tiarti) noiebrKik, 1877-88, 
of whicli (a) and (fc) represent wnrk at Mfliichester, and (c) w 
at Sautb|x>rt. 

2. The material (6) aud (c) has all been now copied oat 
ladi^ftr Ibriii (under aach star), and the l^d;{erii are depusiteil in 
building diU'erent from that containing the original book^ Tl 
muterirtl (a) is iiioru diffiunlt to transcribe in ledger fiirm. It i» 
scarcely possible to baud it to anyono who is not familiar wilb 
variable star records, and procedure is under couhideration. I 
thia opportunity nf Aayiu;^ that £ should be very gtad i>f akiU 
volunteer a-ssi stance, at any rate in dettHng with the copied led 
for ditTcri-itt sCurti, and perhiipii with tiit^ao early i-ecurda aUo. 
any variable star observer has leisui-e for work of the kind ■ 
would L'ouiQiunicale with lue, I «houJd t;ratefiilly accept oasis 
in milking this mass of vahMhki mnteiial ready for pubUcatioo 
aoou as poMtiblu. Unaided, my work rtt it must iiecAssariJy h* 
alow. 

3. The olm'rvati'ms of the elder Btutondell (61815-^18871 
divide themselves inin two periods: — 

1836-1877 at Manchester. "With bis friend Mr Itobrni 
Worthiii«lon, of Cmmpsal! Old Hall, he ereelwl the Crmn 
Observntory, whi-re the large i3«iuch retieotor (the Speculum 
whicli he had himself cast, ground, and polinhetl) was moun 
beside a small s-iiich equatorial refractor" {MonOUy NotiasH^ ilWii 
p. 157)- The furnier instrument is de-Vignated R(t3) below, and 
the Utter A. lu 3/. ;V., xviii. p. 11, the focal iL-ngtb of A ia gir^n 
as 70 inches. Cesidos these a iz-inch ri>fIector belougiug to Mr 
Williamson was u.'^ei), and is desi;;nated U(i2); and other am:^! 
inBlrunionts — a 30-incli acliromatic, a sa-inch achromatic, umi 3 
Tully teleecupe. Thete are calhd ,»o(a), 22{n), and T reAj>BClivf.*. 
There are also B (•' Mr Bowman':* 7 J-inoli ") and C, a comet arvkff 
of alxiut 2\ iit<>he.s a]>eititre. Mr Bnxt-Midell telUme th<it 32{a) wa« 
an excellent af-ineh by Dancer, who also made A. 




J own 



Mar. 1907. ObMnnitions of U Gemimrum, 517 

1877-1888 at Southport, "In 1871 bo was aupoiiiUMl auper- 
intendeiit. of a meteorological ohfu^rriitory in Heabeth Park, fitted 
up antl |)resentet.l by John FurnlBy, Kai]., formerly of Manckestur ; 
and in 1877 liu ttrL^ctoU h'm uwu (irivate ustruiioinical ubeervatory iu 
Bir]{(i:jle, ^><>utltport, ami resunied his ohs'irvatiotm of variable atar^ 
etc with fi 6-inch equatorial refractor by Cooke •& Sons, aasiBted 
for some years (previous to 18SS) by hii* son" (/oc. cit., p. 158). 

4. A carf^fiii note in the qimrt-o \f.S. hook (r.) al)ove givee a 
more d'ttailetl descrijition of the Southpoit Obaerratorj', aud ihe 
folliiwiiig purajjrapLs concern us: — 

•'The obs*?rvat(iry, the oquatorinl iuid micrometer, the portable 
transit inatnimeiit, tiiA sidereal cbrorio meter, and sidereal watch 
belong to Thomas S. Baxley, Esq., of Hatherop Caatle, Fiiirford, 
Gloiicestorsbiit, vrho has kitidly (;rant(-d me the uko of them ro 
long as I may be able or inclined to make n-<<tronomicftl obnerva- 
liona, and ha« alno borne the ex|K!inse of their removal from 
Hatlierup Caallu, aud of tlie re-erectioa of th« obserratory, and 
le-mouiitiiig of the equatorial and trausit instnnnent : and I think 
it a duty to make this record of his unlooked-fur kindness and 
liberality, for which I am moAt sincert^ly and deeply ^tofut. 

'*The object-glast* of ilit> flquatorial i^ 6 inrhes in diameter, nnd 
bas a food lenBth of S7J inchcu. There arw atx negative eye- 
pieces, H comet eyepiece, two reflection sun eyepieces, and tliree 
sunshadeM. Th« powers of the ^ir np^ativa oyepiece*. aa deter- 
mined by Mr Bazley, are. 48, So, 125, iSo, 260, and 360. 

This instrument is denoted by E below. In 1870 and 1871, 
before this iimtrument was erected, he naed Mt Gladstone's 
7j*inch achromatic. 

5. CompartMon Slant. — The brighter comparison stars a, b, r, 
«tc., are the same as those of Fogson and Knott, exi^ept that 
Knott's star I was at t^rst denoted x by Baxendell. As, however, 
there it« no doubt about the ideutttication, aud as he himself used 
I after 1864, I hav(!! (tbtmirh with soma misgivings) altered the 
notebook x into / in what f.jllows. He made one or two deter- 
mination-i of the magnitudes of the brighter star«, but not many : 
prolwitily he accepted these data from Pogaon (or Knott?), and no 
discossioa of his separate observations is necosKary. But see tlie 
letter from Father Hagen, appended to this pa|>er. 

6. As regards faint ntant, Baxendell made some n'* 
observations in the early years. One instance d«wB n' 
observations of th" variable, but may bo given 
indication of what he could see. lie makes the ' 

(I have written ( and tj for x and y to avoid 
another r and y) : — 

" 185S February i. Pogsoti's star c it a d 
there is a fourth star [lerhaps suihcientty m^ar 
quadruple ; $ about 13^ mag. ; 7 about 14 mag. 
light blue colour." 

" 1 858 February 8. Compaaions of Pog» 
13^ m^., 71 about 14 mag." 



Frof. H. S. Turtier, BaacewUlCs 




318 



*'iS58 April 17. Pugaou'x sUic c quudniple ; A 9*2 ni 
B 12, C 15J, 1) 14; C a light Idm colmir, very Kirikiiig foe 
Ktaall a star. Tbi' niagnitndes merely eetitOAted." 

There are nu utlier references to these atan excapt that « 
iliugraru is appundeU on Fubruury 1. thuu^'h wtthuut auy scale. 

7. Now there itt some oonfnaiori about I*i>g8'>n's b and c («i» 
i/. iV., Ixvii. pp. 125-8), Ki>ott iisin^j e and b, where Poj-Bon uwd 
ftpparLtntly /' mid c. AsMumiiig Buxenrlell's idfrntiticati<m to be 
the same an Knott'n, f in tht; double Kt&r £1158; and thi 
pa^ition angle aud apparent ituigoitudes given iu Mr Lewia'i 
rccviit catalu^nitr of the Struve stars &ccurd w«ll with tfau <liagTaiD 
m UflxendoU'e notebook for the pair laarked c This sapplic 
the sciile of the diagmni &p|>r(ixitnate]y, and it can 1:>e accordingl| 
natd as Jollowa (very roughly) : — 









M«i«i. 




I'os. Angle. 


|})Bt. 


Bu. X 


A 





Q*0 


9'a S-S 


3 Oompanton or it 


(333*1 


(7-5) 


12 10*0 


WorC 


130 


9' 


13I 

1 


{orD 


3» 


btf' 


M 1 



lint therti is uu oient^ifn ut either ^ or 17 in Afetnoim R.A, 
vo], Ivi. p. 226. Perhaps aonio double star at>aanrer may care to 
look al £1158 again. (8e<i note by Mr Lewis at end.) 

8. The laiut atuni iu thv uei^hbuurhood uf the variable, oaad 
in compitriiKins, are given iiL a diagram ou 1S58 February 1, wbie^H 
includes Kiintt's /, <;, A, and /, ao tlmt there is no diflivruUy i^| 
reading it. In the ueighbourhnud of U there are no leas ibai 
fi.ce other »tar», two in ink, and three in p'^in.-il |>erhaps added 
alterwardB. One uf thea>t; i« lettered as the variable U, but thi* 
ideDtilicatiun can <>iil)' lie laktfU lu pruvisional, as subsequent notai 
ehow. The bfj'st plan i<eems to bo to give the positions uf these 
xt&nt uH Iteluw (so tliat Mnyiiim can make an accurate diagram foe 
biniuelf in a lew momenta if ha so desires), and the relevant note* 
just as tliL-y Btnud In the notebuuks. For rciidio^ the diagraui, 
the jiarticulurs given in Hageu's AUiu Utelt. Var. have been a««i. 
A Kcale was constructed to tit them as neiirly a£ poraiblr, and iht 
compsriituu of data with results shows the sRill with which 
Baxendell made ?ucb diagrams. 



Jhlar. 1907. Obs9rv(Uions of U Geminorum. 



319 



TAntx I. 



Knoll'a 




QaVeii'i 








BundcUH 




UUer, 


So. 


n I 


A4 


m 


a 


AJ 


utter. 


/ 


18 


-f 3 


+ 5-4 


+ 


D 


+ 5-4 


/ 


7 


as 


+ 18 


-O'l 


+0 


18 


+0-5 


y 


h 


34 


+ Q 6 


+ 4'4 


+ 


6 


+4-0 


h 




23 


+ 7 


-3-8 


+0 


9 


-3-8 


k 


I 


39 


-0 2 


+ 2-1 


-0 


I 


+ 2-2 


I 


k 


33 


+ 4 


-29 


+ 


S 


-»s 


w 
















+ 0-3 


U; ink. 










+0 


2 


+ 0-I 


Peiieil. 










+ 


2 


-03 


Inle. 










+0 


4 


-o-a 


PeUcil. 










+0 


4 


ti* 


Fenail. 



I 



9. The notes are as follows : — 

1858 February i. g^ to gp. Mr Worthinpton'a i^-inch 
reflector. 

A i"3>' '4 or •5>n Qein. 

ft'7>» ■7or*8>U '3 to '5 > rain. vis. 

I believe tha star which I havo marked U will prove to be the 
variable, now 011 it« Tnarch to ano'tber maximum; t)iou(;li very 
SDiall it is di&tinctlj detint>d, lias no haziness about it, and baa a 
dull yellow colour. The abt>v» eatimiitiuns inalce U = i4'o mag., 
tp=i3i7, 1= iy6i, and the vHpisbiiig mag. witli 13 ipchos 
B|>erture= 14*4 tn 145. 

1858 Februnry 4. 7 to 9^ h. 13-inch reflector. 

h '7 or •8>ic "5 or ■6>/. ft [-5 >/ •6>U. w i*o or i'2>U. 
II •4> a sraHlI sur y not noticeii Februnry 1. U is therRfore 
14*3 mag., or *2 or '3 Ivsb than on th^ i«t insU, aitd is p<.'rha]is 
Ihervfors not the variable, y, which ur |H:rha[JB the variable, le 
247 mag. 

1858 February 6. 7'' trt S**. Mr Williamaoii'a 12-iiich reflKCtor. 

/ about '4 > mill, titible. Supi>nacd U and y occasionally seen 
l>y tmiisioiit glimpHUH, and y in |>erha]is the brightoot («ay Ixtth 
under 143 mag.}. 

1858 February 7. 8^ to i)^'^- 13-inch refleator. 
/( ■8>M 'T>1 ■8>auppo*ed U {aay u) '7>y / •4>k '4. 
,*. it.~ 14-5 or 14-6 mag., and y= 14-8 mag. 



185S February 8. S** to 9^^* i3.iuch reflector. 
/ '6>u '3>y a gl]m}>se star nour tu aud following y. 
and y>= 14-7 mag. 




320 



Pn)/. li. U. 'Acmer, BaxendeU's 



1858 February 17. 9'' to Io^ Mr Willtam8an'& 12-in 

reflector. 

A raXr '^>l •6>« "2 or '3>j'. rr still nppenn to 
(let^rensing. The light iif u \sry changeabtf, sonicUmes apjvea 
fully eqita] tu /, and ai otliur Urnes quite disappearing. 
Say u=i4"5 i/-i47'o«g. 




Lxvn. 



,* 
J 




1858 February 18. 8J'' to 9^^. i3-iiicli reflector. 
Iff '4 or ■s>/ ■6>tt *3>y. A io>ie. 
Say u— i4'5. y= 14*8 mag. 

u precedes ff [9**0 and on mme {>arallel ; or, if any difTfmioe^ 
u Boutb, but not to the extent of 5" ; observation diftiRult, a« u 
not bear au illuiuitiation eudicivnt to ruuder tbe spider 
distinctly vieible. 

1858 February 19. 9'' to ro''. i5-inch wflector. 
/(i'orf2>iff •4>( •5>« 'z or •3>y. 

1858 February 20. 8J'' to gl**. is-inch reflector. 

IP '4>/ '5>*i 's or •3>y, suftj'icion of a glimpee alsr near to 
and ftf star u. Fluctuations in the brighineKB of », which 1 bav 
frequeiitly uliservtid lately, are very Htrtking to-night. 

185S Kebruary as. 8^ to 9^ 13-inch reflector, tc and I 
seen occasionally ftretty steadily ; u seen two or three times' 
glimpses, biit no change since last observed. Moon too near for 
very BEtisfact<»Ty ob«ervatiou. 

1S58 February 25. 9** to 9J''. 13-111011 reHector. Owin^ 
the Hining moonlight, I ran only say that U Oeni. ia beluw 13 
Rtar t« gitmpned occasionally. 

185S February 28. $^\ 13-iDcli tefleotor. v and / botb 
occaaionally set^n, but owing to the moonlight, etc. 

1858 March 6. 8^ to lo*. 13-Inoh reflector. 
h 'j>ff -9 or io>ip ■3>/ '4 i>r •5>« '2>y. Fluctuatiooi 
brightness of u noticed a^n to-night. 

1858 Maroh 13. 9^''. y-inch reflector, p. 130. 

w and / occasionally seen pretty Hteudily hy ^impsee, and even 
u two or tjiree timea ?epn in transient glimpaea^ or u and y, &■ in 
thn hunt ^'lim[)H*;H u hail the comfiary nppearance of a very faint 
coarse double star. The difference of ma^. hetweeu tr bjxA I cannot 
be more than •«. 

1858 March 16. S*" to lo^ 13-inch reflector, p. 196. " 

f/ = Qr ■|>A: / i"0 to fa>A: w ■4>/ '4 or'5>tt 'z>y. 

Occasionally a su-npiuion of a Hiuall companion ef u about t«j 

distnnt. 




Obsitrvatiuns of IT Oeininontm. 



321 



185S May I. 9^ 25"*. i3inoh refipctur, p. 199. 

K '3>t. When u tir«t Iwcame vwible in the twilight ( wa* quite 



invisible. 

l = or>u: 



JO" 



40" a '2>i. lo"* (after iiiterrujilioa by clouds) 
10"" / '2 >u: »r ■6>«. 



185S May 3. gj*" to joj''. 13-inch rafloctor, y. 199. 
If -4>/ '4>u '^>y. No ititlicutious of auy minute 

H, altbouj^h carefully looked for. 



sUr near 



I 
I 



1853 May 4. 9^** to toj''. I3'inch reflector, pp. 199 ami 350. 
IP 4>-t '4 or •5>« '3 or •4>y. Could not satisfy myseU of 
the exiit«Dceof any minute Htar near ». 

1858 November 13. 12^. 7-iiich reflector, p. 130. 

I glimpsed ; twu or three transient glimpses of u. f U 14 mag. 

1858 NovBmber 14. 12^ y-iuch n^tJKctor, p. 40. 

U Gem. has auddenly hurst forth, ami is now ~ Pogaon'a 
6=9*3 ^^H- ^^'^it^ puwiT I 30 it in mui;h Iuhs sharply df^Bnori than 
a, b, or r!, and compared with them ban stimewhat of a nebulous 
appearance. Its colour ih white. It appears tu be exactly on the 
place of my star u. 

1859 Febru'iry 27. 9''. 13-inch reflector, pi. 199. 

/"S>U ■2>/(U I2"2 mag. Neithnr wiili ai-hrniiiatic p. 223 
nor reflector pp. 199 nnd 300 is U ro well itufined aa the neighbour- 
ing Btan ; but 1 tliiiik it ta not so hazy-looking as it was in 
NoTBmber last jr only Heen by gUuip«i:», atid no star «eeu or 
HUBpcctcd near IT. 

1859 Februury 28. 13,^. 13-inch refleotor, pp. 199 and 300. 

U •2>Kf/t •8>U .". U i3"i may. No email star visible very 
near U, and from the poAition of U with reapect U> w, x, and y, I 
can have no doubt that U and Winne<^k(!'s Ktar are identical. U 
white or bluu'h white ; light steady aud haziness still perceptible. 

1859 April 22. q}^'. i3-ini;h relkctor, p. 196. 

I '4 or '5 >ii "3 iir -4 >jr. From the position of u with respect 
to w, /, and y, I have no doubt it is the variable. It has, however, 
a ruddy appearance, and is, when ht»t seen, very sharply deSned. 

1859 November 30. t3-inch rattector, pp. 81 and 196. 
If and y both seen. U below 14-2 mug. 

This last QJte is interpreted to mean, "if U is not the same at 
«, it is below 14-2 mag," for it seems clear that Baxondell eop 
Mdend u to Im the variable. 

10. TheM are practically all the notes thxt help in any v 
identify the small 8t.irs. When, as on 1858 February 28. 
light or haze interfered, the note has been curtailed, and gf 
notes that do not help us have been omitted. The comptr 



3*2 



/Vo/. ff. H. Turner. Btacndelta 



these imall stars are collecttMl Iwlow id Table II. It will ba 
ihat Baxeudell obiierved somelimea to 0*05, Uiking his unit 
approximatelj o'l magnitude, winch bj c<>m|>arisoa with Hi _ 
raiignitud'Q8 ve see it vnrv nearljr correct. Adjusting tiiedifTeicaott 
t4i til tht< fimr litars {?, h, w, ^ aa nearly a* poasible, we hare — 





as=ff 


M=A 


33- w 


39«' 


Ha^n 


ii*( 


1113 


12*1 


12*6 


Baxeii(ir]1 


11 -OS 


IIIO 


12-05 


12*45 



Lxvn.5. 

1 UmM 
■' unit ^M 
I Hagu^R 

I 



12-90 i3*ao 

And v« maj compcLre with these fiaxeiidell's own abeolut* deter 

Itiinations for u and y, viz. u= 14-5 (four nights), t/» 14*8 /fonr 
iiigljt«); didwiiiK that his adopted magnitudea are in axcess^ m] 
indicated uhovo in the case of ^1158. 



L 






Tablb a. 






^ 


P 




BaxtneUtPi Compartiam </ ^in4 S2ar«. 


■ 


DKte. 




ir 


A * 




1 


* 


1858 F«b. 


] 


... 


7 


... 


4i 


•»r 




4 


... 


7\ 


%h 


6 


4 




7 


... 


B 




8 


s 


1 


8 


... 


... 




6 


3 


1 


17 




12 




6 


>i 


1 


18 


... 




4j 


6 


3 


] 


19 


... 


II 






*l 


■ 


20 


... 


... 






s4 


Mar. 


6 


- 1 


II 




4i 


a 




<3 


- 1 


... 






*■■ 




16 


+ 4 


... 




4i 


a 


Apr. 


I 


+ 1 


10 


^h 


4* 


4 


k 


4 


+2 


9 






S 


1 


6 


+ 1 




4i 




5« 


1 


10 


+ 1 


... 


4i 


3i 


..- 


r 


13 




... 


4i 


H 


■•• 




17 


... 


... 








May 


J 










3 




4 


... 


... 




41 


Ji 




s 




... 










6 














10 


... 


... 




3i 


31 




ir 










■ •* 


1859 Apr. 


22 
MU 








4i 


3) 


»( 


+ 105 


+ ^95 


+ •40 


+ ■45 


+ -30 




Obtervatitma of U (rBtnijiorum, 



323 



ir. The Obgerixitiong uf the VariaMs. — ^The ohservationa are 
jcoliectad in Table III. in a concise form. Baxeiidell iiBe<l tbo 
taymWl > tu bis nolubooks ; but as it can alwuyti bu inferred from 
}tlic order of the other ayiubols, it Irns been omitted. When he 
^nveft alternative r&adings tiicti as -5 or *6, the moan has been 
taken. Finally the decimal pointtt have been omitted. Tims his 
record 

k "7 or 'Sxp "5 or •6>t 



^iKCOines 



/. 7j <P Sh '■ 



Other contractioiiA wiU be readily undL'ratuod. Thus on 1859 
May 20 the inference <i+ 15 means* that the faitilfst star visible 
wait judged to be a magnitude and a half fainter than It. 

The letter u has been retalDe-Ll where Biuceudell used it, 
although he aftern-ards decided that it vma the variable near 
minimuni. It »eeni» adviNable tn indicate as closely as poesihle 
the gradual exploring of the small stars by keeping the notebook 
records. 

12. The early observation tt are difTicult to ^ive in tabular form, 
end are better simply tnmscribed aa follows;— 

1857 February 25. Mr W.'k 5 in, ach. p. 6S. Several veiy 
small stars about the place of U Gem.; but all much l<v.s than 
the «tar to the soiith, about 9^ ma^. 

1857 March 4. lo**. With 5 in. aclir. Star* not brighter 
ihan 1 1 mag. in the [ilace of U Gem. 

1857 March 8. i r**. With 5 in. ach. p. 68. A star of about 
1 1 mag. in the place of XT Oeni., and another near it nf 2' or 3' 
distant iLud about half u nm>.'. leas. 

1857 March 16. About S''. 5 in. ach. p. 68. No star brighter 
than 1 1 nia^. abuut the plu>'e of U Geui. 



1857 March 21. 
place of U Gem. 

[1857 March 24 
April 13.] 

1857 April 13. 30 in 



11^^. 30 in. ach. N'othing visible in the 
is the last date in the book preceduig 



ach. A very minute star occasionally 



^'isih|p about the place of U Ocni., and therefore about ia4 iiiai^. 

[1857 April 14, 15, 16. Other stars observed, but U Geia. 
appiircntly net looked fur,] 

[1857 April iS. 9^''. 5 in. ach. A diagram is made of the 
stars/, k, <j and three brighter (Hagen's 18, 24, 35, 22, 21, 19), 
aud the rciuark made "small cumpauion of /" (that is A= ii'o) 
"almoat u jnin. visible, and therefore about iih mag." Baxeu- 
dell's magnitudes are too lar^e, as shown eisewiiere.J 

1857 April 19. lo**. 30 in. ach. Nothing visible on 
place of U. Ilem. 

[1S57 April 20. lo^ 5 in. ach. p. 68. Sketch of Ap 
refeti-ed u\ and Hajj^n's iS judged "i or '2 brighter than 21. 

13. There is nothing more before October, and the obeer* 
from this point may be given in tubular form. 



r 


324 


1 

Pn/. H, H. Turner, BaaxnddVs UVl^ 


^^^ 






Table III. 




1 


^V Dp la 


meMopa 


Uli«*mittuni and 


!>•*- 


Tslwcops Ohfl 






■nd Poww 


liifersDcM. 






ftDd P<i«w. ui 


1 '*S7. 








1558. 






■ 


b b 






d 


b b 




H Oct 38 




T35 


Nat seen. 


Apr. 12 


9i 


A 40 Kot M 


I Not. 1 8 




T35 


„ <ino. 


13 


84-94 


B(I3)I96 /34-. 


B 




., 


., 


I? 


9-11 


H<i3) '99 '4«3l 


H 36 


"i 


• • 


,, 


21 


9^ 


11(13)196 Nglm 


1858. 








33 


94 


B(I3H96 •. 


Jul 20 


9i 


A6S 




n 


9 


K(i3)i96 NoCM 


21 


»3 


T3S 




Mny I 


9i 


B( ■ 3) 199 Sm the 


aj 


Hi 


T40 


., <ft+ia 


3 


94-104 


R<i3)3SO '4«31 


31 


10 


R(l2) 


„ <i3'a 


4 


94-104 


R(»3)'w Uka| 


Feb. 1 


91 


R(i3) 


Ui«: W74«4 


5 


9|-ro4 


R(U)>99 '4^ 








limit. 


6 


10-104 


ff.i3)i99 '4» 


4 


7-9i 


«(I3) 


tbu:wi\ U4y. 


to 


10-104 


K(I3>I99 '34"J 


6 


7-8 


K{12) 


«=y. 


11 


10-11 


R(i3>i99 i4«. 


7 


8-9i 


RC«3) 


/ 8 » 2 y. 


16 


10-104 


R(i3)i99 NolOT 


8 


8-9i 


H('3) 


f 6 1* 3 y. 


18 


10-104 


K('3>»99 ju 


17 


g-io 


K(I2} 


/ 6 H 2 j y. 


&«pt 20 


15 


R(i3)i96 «^ 


iS 


8^-91 


mi3) 


/ 6 u 3 ». 


Not. 2 




(33)a Nan 
(33)0, 21 J| 


»9 


9-10 


IK 13) 


i 5 " 24 y- 


5 




*o 


8i-gi 


R(i3) 


/ 5 M 24 y. 


6 




(u)a. 31 fl 


23 


8-9 


RCi) 


Not fte«n<f. 


to 


12i 


U(7) 130 ■ 


25 


9-9i 


K('3) 


„ <»^ 


It 


.24 


B(7) 130 ■ 


26 


8| 


R(i3) 


.. <w. 


la 


124 


B(7) 130 u gUiq 


28 


8^ 


K/13) 


M <f. 


>5 


12 


K{7)40 D«A. 


Mar. 3 


9 


T35 


M <f. 


16 


II 


R(7)40 ftllli. 


6 


8-10 


R{'3) 


/ 44 " a jr. 


17 


11-11} 


"t7)40 ^ .p 
130 J *^»*' 


II 


iti 


A68 


Nat sv«a</. 






13 


9k 


B<7) 130 


.. </. 


18 


'3 


R{t3}8i fttaUi 


( 

1 14 


8 


A 68 


,. <-^ 


21 


124 


R( 1^)199 Kotw 


! 


8-10 


B(i3) 


M4«21,. 


Dec. 2 


94 


11(13)199 M 


1 *» 


S-ia 


A 40 


Not Mfll < IT, 


1859- 




1 


** 


8 


RCii)8i 


„ <12-6. 


Feb. 22 


104 


A6S o>H 


36 


Si 


R(i3)8i 


<ff. 


*3 


12J 


[22>aai cJD?l 


Apr. I 


8-10 


R{13)I96 


i44'*4y. 


14 


7 


A 68 <=>U. 


4 


8i-9i 


R(i3l'96 


' 4 " 5 >■ 


26 


i>i 


{aa>i «-sU. 


6 


8i-9j 


R("i)i96 


0«5ly- 


37 


7 


A 68 /7O3 


L ' 


9& 


H<7)40 


Not wen. 


«7 


9 


K('3)i99 /8U2 


L. 


84-10 


B(I3>I9* 


1 34 u 4 limit. 


38 


13 


B(t3)3C» AfUi 



Mar. 


1907. 


Obseifttlions of V Gem 


1710 f-um. 




^ 

32s 






Table III. — tuMimwl. 






D*lF. 


TelMOopo 


niiturratkina luwl n 




Telescope 


Oliwmifaim and 


and Poiror 


tnlcrmon. 




■DdFowcr 


lof^nncea 








t86i. 








h m 






d 


ti m 






. 8J 


R(i3)3«> 


VM«1I. 


Jao. 6 


9 5 


A68 


Nol ■«eD< i3*a 


■ 9l 


R(l3)i9« 


* 4l « 3i y. 


>5 


10 10 


A6S 


.. <'3'3- 


[ lOi 


A 40 


Not HMU. 


3& 


9 35 


A 68 


< 1 1 'O. 


i 10 


A 40 


., < 1 1 0. 


Feb. 6 


la 35 


O39 


„ <i2-a 


> tQ 


A 40 


„ <6+i5. 


10 


9 5 


A 68 


.. <'3*3- 


I loi 


A 40 


„ <6+i5. 


M 


7 40 


A68 


.. <II'0. 


1 t<^i 


A 40 


„ < 107. 


38 


10 25 


C39 


„ -ciiu 




K{i3li96 


H aud V Men. 


Mar. it 


10 15 


C39 


., <io-5. 


1 


A 68 


Kot BMn < iol 


13 


83s 


IMi3)8i 


isu. 


! 


8(13)196 


., */. 


16 


10 s 


A68 


NolRfeii'. 1 5 -3. 


\ 


R(I3)I96 


H ■nd y Men, 


21 


S 30 


A68 


.. <9-5 








30 


S35 


A68 


.. <i3'3. 


i to 


R(i3) 199 


15 U. 


Apr. 3 


9 10 


A6S 


.. <I3'3. 


» 9 


A 68 


Nat M0a<ui+. 


6 


8 30 


A6S 


.. <ia-5. 


i 9i 


A68 


.. <I3* 


9 


10 40 


C39 


>. < lO'S- 


t 8 


A 223 


.. <iro. 


10 


10 30 


E(i3)i96 


/4U. 


i 8 


A 333 


.. <13'«>. 


11 


8 50 


A 68 


Not BMUC 13*3. 


t 10 


R<i3)'99 


D- i4'3- 


14 


9 30 


R(»3) 81 


/4U. 


1 9* 


A 39 


Nol H««u<io'3. 


so 


8 30 


A68 


Not Men < 1 1 -a 


1 9 


A 233 


.. <J37- 


38 


10 


A 68 


.. <I3'3- 


> 10 


R(i3) 


<t4'a 


May 4 


10 


A6S 


fl2U3c; D3J*. 


' H 


A6ti 


,. < lyo. 


9 


9 30 


A 68 


6 2 U ; c a C. 


i lo 


A 68 


» <t3'o- 


»3 


9 30 


A68 


Kot MeD< ID'S. 


> 9i 


A68 


uzU. 


14 


10 35 


A68 


U4/. 


1 9 


A6S 


«35U3«. 


Oct. 2S 


II 40 


.. 


Not ■««]< 12*$. 


i 9 


A68 


a3U4ic 


D«c. 38 


9 


•• 


VBliMml, 


t 9 


A6S 


a6Ulc:Dii<6. 


I%I62. 








\ 9i 


A68 


oi)U:biT7. 


Jan. 5 


9 15 


>• 


a8U: «lUifl; 


i 9 


A6S 


()liU:6iU. 


10 


9 30 


., 


TTiBible< to'i 


9 


A68 


» 2 U : a 10 Cr. 


II 


8 '5 


,, 


^^ 


lOi 




/4U. 


33 


8 IS 


■ 1 


.^^^L_j 


1 9i 


B(I3)I96 


tfloU: 


Mar, ts 




,, 


^^^^^kri 






h7\\3zhtp. 


'9 

22 


10 
9 


M 


^^H 


to 50 


C39 


Not ■MIKID'a 


31 


lo 5 


>> 


^^^^^^H 


\ U + 


H(7)39 


„ <ii*3. 


A|jr. 8 


10 30 


. 


^^^^^^H 


1 9 + 


A68 


., < 13*3. 


ID 


8 35 


- 


^B 



w 


3*6 


Prof. H. H. TurrufT, BoMndelVa 


LXTO.^ 


^^ 






Tabls fll.— tiOKfunierf. 




I 


^V Ditc. 


And Powe 


ObwrvsUutiB Mid 
Infnnnn*. 


D>U. 


Talaaoop* 
■ndPoww 


.<J 


1 1863, 

w 


h m 






1861. 

d b u 




■ 


H Apr. It 


8 so 


A6S 


Not »e«n< lO'S- 


Apr. 15 9 


A6S 


NatWfti 


^m 


... 


•1 


Suipccled <: I ra 


Not. 3 12 q 


., 


.^ 


■ 




n 


liot MCD<: I2'0. 


4 13 30 


O39 


,s 


H 


9 "S 


>l 


OIiniii»«l< Ij'l. 


5 <2 40 


>t 


^1 


1 


10 


M 


Tglim]iMd<i3"5. 


8 13 30 


„ 


'^1 


H 


10 30 


,, 


Not scci)<i3'3. 


Dec 3 tj 


>• 


^1 


H 


9 45 


,, 


Not »eon<i3"3. 


S 10 15 


A6S 


,^1 


■ Hay 3 


9 45 


B(i3)8l 


Barel? KUtnpswi 


17 8 30 


■1 


^1 


H 






<i3J. 


27 7 30 


(< 


641^1 


B 


10 30 


A 68 


Not M«ii<t9'5. 


39 9 30 


C39 


Xotfl 


■ 


10 10 


A68 


„ <ii'a 


1864. 




fl 


H Oct 18 


13 50 


C 39 


,, <io-5. 


J&n. 4 8 30 


A 68 


•9 


^^ Nov. 15 


13 10 


t. 


,, <io"a 


Feb. 12 


„ 


■j^^H 


1 


10 to 


R(i3)8i 


.. <i3S- 


Uar. IS 9 10 


■ • 






9 


A6S 


<I3'0. 


33 940 
38 9 40 


>• 


1 


1 


11 30 


.. 


Not HMI|<I3'3. 


Apr. II 90 


•» 


^^ 


1 


14 


«■ 


„ < 13*2. 


13 


■ f 


^1 


1 <863- 








18 


tt 


.9 


H Jan. 33 


7 40 


,, 


.. <i3*3- 


21 


*t 


.S 


■ Fob. S 


7 SO 


II 


GHmpfted ? 
<I3'3- 


25 

38 


• • 


Stt^wM' 


^H 


II 


I' 


Not 8Beii<l3*3. 


May 7 10 10 


■ 1 


Via mm* 


1 


9 


C39 


„ <i3'a 


Oct. 7 


H(i3) 


QVbMigmi 


H 


9 


A6S 
B S8 


.. <I3*3- 
.. < 14*0. 


3' 
Nov. 5 


A68 

R(i3) 


N0C«MA' 

DoabtU- 


^v 


8 10 


A68 


.. <I37- 


28 


A68 


"1 


B M»r. 3 


9 40 


,, 


,, CII'O, 


Dec. 31 


<t 




II 


I > 


.. <i3-3- 


30 7 40 


tt 


ftlU=t 


^1 


II 


!• 


<l3*o. 


31 <> 10 


(■ 


«6^ 


1 


9 


II 


.. <'3'3 


t8£s- 




■ 


■ 


845 


■ t 


.. <'30- 


Jan. 4 8 30 


«. 


aiiU^ 


H A|)r. 


9 30 


.. 


„ <I0'0. 6 


i> 


ei\V. 


H 


8 40 


• ■ 


6 3 U 6^ t< : 
U I4cc3ir. 


20 

Mar. 30 


)i 




■ 


9 


II 


,2\\Uf: 


Apr, 10 


,, 


■ 


t 






<i6\\3. ' \S 


w 


J 



Mar. 1907. Ohaervaiions of U Geminorum. 



327 









TabLB l\\.—cotUinttmU 








Data. 


Teleacope 
uid Pnwer 


ObHrvMloni nnd 
Infer«BC«s. 




Date. 


Teleaoope 
and Power 


Obserratlona and 
Inferenoea. 


d 


h m 






1867. 
d 


ta m 






»• 


to 


A6S 


/9U3A:Ulff 


Not. 


17 


... 


A68 


Not seen < 13^ 








I2*r. 


Dec. 


18 


8 10 


,, 


U2/. 


*5 


10 


.. 


94U12 6. 




22 


850 


,, 


Not ae«n< 13*8. 


36 
31 
14 

33 


10 


It 
■1 


A I UI3-4- 
NotseeiK 13 "3. 

.. <I3*3- 

„ <I2-5. 


1868. 
Apr. II 

23 




11 


" <I3 3- 
<:i3"*. 


36 

16 
18 


9 40 

10 35 

13 30 


It 
C39 


.. <'3 3. 

A6iU5*,!?4U 

12-9. 
a6U2c;U3ft. 


1869. 
Feb. 5 
Map. 2 
Dec. 23 

187a 
Mar. 25 




It 
II 
>> 

O60 


<I2-8. 

.. <I3*5. 

'3iU. 


30 


8 15 


A68 


a6iU26jUiJc. 


187 


. 








33 


7 10 


,, 


e I U, 6 li U. 


M«r. 


>3 




C39 


Not seen. 


23 


II 20 


,, 


a6UiJ6;U2c. 


Apr. 


7 




G 


11 <i4'ft 


38 




,, 


Not seeD< 10*3. 




10 




II 


.. < 137- 


39 




.. 


„ <io-5. 


1877. 








3 


8 40 


>. 


t4iU; / = U 


Dec. 


12 




E8oJc 180 Notseen<i3-5. 


- 13 




,, 


137. 
Not seen < 13-5. 


1878. 
Jan. 9 






.. <i3*o. 


- 13 

31 
33 

• 9 


9 50 
10 30 


•• 


.. <'3*3. 
/3U8A. 

A4iU. 

Not Men<l2j. 


Mar. 
Apri 


24 

31 
I 

5 




E80 

II 


.. <'3*5- 
.. <'3*5- 
„ <:i35- 

Glimpsed 137. 


57. 










6 




,. 


Barely glimpsed 


3 




t) 


.. <I3'3. 




8 




,, 


NotHeeiK 1 2 "5. 


8 




■• 


Suspected < 13*3. 




17 




,, 


.1 <I3'0- 


II 




•• 


Not aeen< I3'3, 


ftlay 


1 


9 40 


,, 


/6U4/(;U7ff. 


16 




• > 


,, < 102, 




3 


10 30 


,, 


Not seen-ci3. 


28 




• t 


.. <i3'4. 


Nov. 


2 


J I 50 


,, 


■ . < 


», 2 




.. 


.. <I32- 




4 


5 15 


,, 


,, 


30 




!• 


„ < 13*0. 




25 




,, 


J 


36 




• > 


,, <I3"0. 




28 




,, 


ij 


r. 31 




II 


,, < 13*0. 


Dec. 


7 




,, 


,, 


y 5 




C39 


,, <io-5. 




23 






II 


14 




A68 


,, ■<:i2'a 




30 




,, 





328 



Pro/. H. H. Twnm, BomiuUIFm UETSL 5. 





I 




Table IIL 


— ceiih'tiiMiI. 




DO*. 


TU«Mapi ObwrfattoBi ud 


D*U. 


OtgrnjteMi 


«879., 








i88a 






4 


li ■ 






d 


h m 




Jaa. 13 


740 


S80 


&2U: ciUi 


May 6 


10 ao 


NotK«B<l31X 








aioU. 


9 


... 


•t <f. 




8 


II 


bi\J=e. 


10 


10 40 


» "Cfc 


JS 


6 50 


If 


»liU;eiU 


la 


1035 


» <«S'S. 








a lot U. 


Oot. 9 


la 40 


•t <*i 




815 


>■ 


btlViciV. 


10 


13 ao 


„ <*. 


16 


8ao 


,. 


biUicaU i^e. 


Nor. 96 


II 30 


*5n;<a4U. 




8351 
9 45^ 




ai^Viod. 


a? 


12 4a 


=*I37. 






Deo. I 


10 15 


Notaan<t: 


19 


7 10 


... 


U4«;U7i/. 


a4 


9 ao 


/loViif t I^4lJL 


32 


830 


K80 


A7U3Jfc. 


as 


8 as 


Ua*;U5i. 




8 40 


Ei25 


k&Vik. 


1881. 






as 


9 45 


E80 


l-iVal. 


Apr. I 


850 


ftoVthlg. 


as 


10 30 




Xot Men < 13x1 




»< $S 


Uii/:tria4*. 


April xo 


9 <5 




NotieBD</-<-3. 




12 14 


U4/; U3«i <aU 


Htpt.19 


1430 




» <*+3. 




» 3S 


Us/:*rf«*IT3«. 


Oct 14 


xa 50 




.1 <i3-5- 


a 


8 IS 


Uit:s5 IT. 


15 


13 




M <*+3- 


3 


9 S 


«5iUxJ|fr:U|& 


ao 


13 




1, <^ 


5 


8 40 


frlU;e3n':n7U. 


Nov. I 


12 




<A + 7- 


6 


10 40 


AiiU; e341T; 117 


iHHol 








7 


9 5 


6iU:c2U. 


JtD. 18 


12 




Glinipeed=i3'5 


8 


835 


b^V-.esVatoVl 


19 


It 




NotMen<i: + 3. 


9 


9 IS 


bjJJSd: at3D:f 


sa 


12 1$ 




,, <i3*o. 


17 


9 10 


NotM«D<i3*aL 


28 


7 




(19X7=6 lie 


0.t 26 




M <*. 


29 


10 40 




6 = Uo8U. 


Nor. 14 




.. <I3'S- 


31 


12 20 




ri U lo) d. 


17 

Dec. 27 






Feb. I 


9 30 




6iiU;riU. 


1882. 






3 


7 10 




&4 (J 5d; U IOC 


Mar. 6 


815 


/5U4?:D8*. 


S 


9 »S 




rf a U 5 r. 


8 


II 20 


Not mmkA. 


8 


9 




AJU:ff7jlT. 


12 


12 


GlinpMd<f. 


14 






Not ■e«n<<r. 


Oct. 28 


12 


Not MOD <i. 


Apr. 29 


10 




„ <I30. 


1883. 






30 


II 




(ilinipMed 137. 


.IkD. 30 


7 45 


a5V = b. 


Hft7 I 


9 50 




Not HMII. 


18S4. 






3 


10 45 




GliaipMtliJraiU. 


J«n. 30 




Not leeiKi:. 



[ar. 1907. (^iermiions of IT Geminonim, 



329 







Tablb ml 


— rtni/Mi«rt'. 






Uftto. 


OliMrrattoni und 
Infcraoen. 


Uat>. 


ObMrvaUoiii bihI 
InhreiKM. 


1884. 


h ni 




iSSti. 

>1 


li m 




Teb. 2 




y!<iXamu<k'*-2. 


Jm. 31 


... 


Not »een</. 


11*7 18 


10 30 


ei2tJ5t:d3tJ. 


F«b. 14 


... 


.. <!»:AS?- 


19 


10 ao 


rf6U4i«-«l7U. 


23 




ft 


Dts. 20 


12 o 


/su. 


Mar. 3 


" 5 


JtsUi/. 


tSSs. 






6 


8 


fr3JU;c2U8tf. 


J>n 5 


10 30 


MjUaU. 


7 


8 30 


A4U; eaU. 


6 


7 35 


/i3U2A:Uiu. 


8 


7 55 


fc2iU:eiD8iri. 


7 


10 5 


16U7/:j5ns*. 


9 


7 50 


J<iir=e;Uiorf. 


8 




1-3 u=/. 


10 


7 45 


frjU ;«i Uiorf. 


Uar. 22 




Kot wen <t. 


II 


7 35 


^4*^1*3108^/. 


M^- ' 




., <i. 


12 


7 5« 


66U:c5U7rf. 


S 


8 40 


«7U-fti Uiic 


Nov. 30 


'o 5 


i = Ulir. 


_ Kov. 15 


11 


Niit»mi<i2'5. 


D«o. 1 


II 20 


i = Uiic 


Udw. 1 


10 u 


., <i3'o- 


4 


9 5 


c4U7d. 


1 ISS6. 






4 


10 15 


eiiVjdi^S''' 


■Ju. 4 


... 


,. <i3-5. 


1S87. 






I s 


10 SO 


.. <'37 


Feb. 26 


8 


»1.01lt=/. 


1 ^ 




., <t 


27 


h 


/7U3A. 


1 "" 


... 


„ </. 


38 


9 30 


*loU7t:/8Aip. 


^P [Tbi only reniaiiiiDg entries in 
^B^JiiTM T faiifl bIai-1 Jnnii lo /lira tbirH^. 


i,h« book are 
Pram iS^a 


on Marcb 3 (tliiw aUn), 
Aliril tlinn> urf nn •n«r!'il 



I 



rutria alioat th« iclctcop*, wbkb qiajt b« auunied to be K tbronglitnit,] 



The roUowtng letter from Father Hageti explains ii^eli. He 
drawis atteolii>ii to an unlucky misprint iu my \myvr uu )t. 128, 
TLK. I'rigsfin's number for m m L)ie fir*t cnltimn i^hotiltJ be, n ut 113, 
but 115, as in tha diagrtm. Alter - ■ -it" ~^ 

aiisume<l ihal ltaxeu«ioU'i k woa not 
(Hagea'ti 23): uud Baxcndcll moat li - 

(Uagen'a 33). The iitentitiu^tion uf tht'-^- ' .^^i.r 

troublesome. 



«u*j DC, nui 1 1 3, 
idu^HBgHM 




330 Ptof. H. H. Turtier, Baxtndtll'g 

Ltiler from Faihn- flagen an the Cumparisan Star* 
for t' Gemirurrum. 

My Dear Professor Turutr, — Your i-ubticntion of 
observations of V Oeminorum in the MonthUj Sotifr^, vol. h 
pp. 119-131, will ])rovo very useful to studt-iiis iiit«ro8te<l in Ibu 
line u( utttroiiouiy. The piiblication might perhaps be euhaorcd m 
Its value by it few ntatemetilH n-'t^arding PogMm's coinpa,risoD ^tan. 
In tiiakin^' a Goal discussion of Pogson'a obet-rvationa, one mil 
uatumllv not be natiefi'^d with the idontifiralion of tfae coiDpextaoti 
stent from diagrams alone, or with the prelimiiiajy magnitodM 
asaipned lo them by Pi»g!ii>n and Kiintt. 

The exact identiliLation of all the stani of faiB chart was inadi 
by FogHoii liiniHcIf in w maiiu)icri[>t ciitaloguo now preserved at ibe 
Harvard CuUe^ite Observatory. The c-ntalogne wa* made witLiu 
the years 1836 to 18^0 at the RjidctilfttandHartweil Obeervatiinf^ 
On hve pa^fs it ^ive^ the H.A. and Decl. of all the atan od the 
chart, reduced to i86o'o. A complete illuatratioa of Poison '1 
catalogues iiiiiy tic H^icn in a publicAtion of (fporgetown Collemt 
Observatory, entitled "SuppleniKiitJiry Notes, " eic, p(». jS-ji 
There is no chart of this Variable among the inaDuecripte pre<«rvt:ii 
at Harrnrd. It in, howerer, nut uece^sury to cooauIl the** 
naanti.scrlpltf, since all of PogBoii'B comjiariHon star* of l 
deininvrum can be identiticd by nteana of chart 3815 of Ibt 
AUai< Sfel^arnm Variafdlwm (SerieR 11.). 

An 10 I he iimguitudflB of the stars, those of Pogsun and KdoQ 
hikve apparently a common ttcale, au<l seem to bo baaed on lb 
tlieortilicdl limit of visibility in their irislruraenl«. llie Ubk 
subjoined give;*, in addition, the ma^'uitudes of the fairilvr sUff 
by Winnecke, and those <jf ujl the stairs, computed from the pwir* 
i>f the A.S.V. The htter two setM of maKiittudea have i^iJm a 
ciimmon Acale, and arc both ba3c<l upon the B.D. system. 

The hrsl two columus of the fuIlowiii>! lahlu explain thoa 
selves from ))a^ 1 z8 of your article. The third giveft the leltm 
and magnitudes of Winnecke, and is taken from the Atttr. SwKt.. 
vol, xlvii. N'o. IT20. The two colmnaa headed A.S.V. cnnuic 
the nuinbera and luagnitudes of the atlas chart 2815, From thi 
same alios are taken the columns Aa and A£, which give tk» 
poflitiouN uf the comparison stars relative to the Variable in K.A. 
and Decl. To them are appended two columns />, with thr 
mean result^i deduced from your readings of the two diagiaas. 
They may servt to show, on the one hand, bow accurate tbf 
diagrsms are, atid, on the other, thnt there is ao doubt left in Ih* 
ideatihCHtious.* 

• In voL ivii of the Anlr'tphynietiJ Jmimnt, p. iSl, I HQijaeaud 
Pofgsoii'a ^tal■ 8-9 mif-lit be No. 5 of tii« Atlas Chart, iostnurar Jf 
indJ^DK (rom th« b.R magniluile of this atar, and not baring ttt%u 
diagram. 



»r. 1907. ObservcUvms 0/ U OwjinorKW, 



331 



roflMR** Cbff^Afitm SUm for U OmiiiuirHm, 



Ri8*on. 


KnoU. 


WinDAcke. 


AAV. 


Aa. D. 


u. 


D. 


fiu. 

1B.H.T.] 


U 
a 8-8 


a 


M 

8-6 


M 


t 


8« 


m I ■ 

+ 047 


- 19-8 


19*5 




h 9*2 


e 


9-a 




3 


«'8 


-f 1 26 28 


- 6-9 


7'o 




e 9*4 


& 


93 




4 


9-0 


+ 1 19 20 


- 96 


9'o 




d 10-3 


d 


IQ'3 




9 


9-6 


-1 10 II 


+ 14-5 


U*5 




» 10'2 








11 


9-6 


-0 46 46 


+ 167 


16 




* lo-S 


r 


10 -6 




16 


lO'O 


-0 27 27 


- 9*9 


9'5 




/>'-3 


f 


II '2 


/ io'9 


18 


io'3 


+ 2 I 


+ 5*4 


6-0 


/ 


m ii'5 






ff 107 


23 


10-8 


+ 074 


- 3-8 


5 


k 


A 13*3 


h 


IJ-J 


« irj 


»4 


lit) 


+ 066 


+ 4*4 


4'5 


h 


8 l''9 


9 


11*3 


d 11*4 


25 


il'l 


+ 18 18 


- o-i 


+0-5 


9 


( 13^) 


k 


IJ3 


fc la'a 


33 


13*1 


+ 4 5 


- 29 


I "5 


w 


A! 137 


t 


137 


a I2'6 


39 


13*6 


-0 2 5 


+ 2'I 


2 


I 



One word I wish to odd about the remarkable fluctuaUoD of 

light in tliie Variable an npfin by I'ogion on March 26. 1856. 

Attention has been called to this record, in substantially tlia aaiue 

words, by Mr J. BaxemlcU in tlie A»(rotiomical J'mnutl, vol. xxii., 

ti>o3, p. 137. In the year following I had occaaion to illustrate 

KPogBoa's obeervattnn of 1S56 by four other itistauces of a similar 

^f nature, and to Ruggest that insUmtanoaaB fluctuations in the light 

of Btara, when recorded by good authority, should not be rejected 

AS uncoufirmed (see Astrupkyiicai Journal, vul. xvii., 1903, pj>. 

JaSi-iSs). — Vei7 faitbfvilly yours, J. G. IIaobn, S.J. 

Sfteeiu Vaticanat 
Jamatry 27, 1907. 



Note hy Mr Letcit. 

The erening of 1907 March 11, on which I refreived the proof 
)f Profesaor Turner's paper, boing fairJy ^oud, the zS-inch mfractor 
Lwas aet on ^ 1 158 and measures made of the faint stars near. The 
ETesolts are : — 





Hagnttaikt. 


F<Mlthin. 


DlstancA. 




AB, 


8-5 and 9-8 


33*^ 


774 = 


2 1158 


AC, 


8-5 ,. 12*0 


256*0 


iS*70 




AD. 


8*5 .. I30 


3047 


65 '30 




AE, 


8*5 M 13*5 


154*2 


58-35 





.The measure of AB is a mean of Mr Eddington's aod my own. 
|The measures of C, D, E are by myself, — ^T. Lbwib, 

Z6 



I&tto 



332 Ptaf. H. H. Tumtr, On the CUusijicatian of lxvil 5. 

On the Cinaification of Long-period Variable Startt, axd a pomihk 
PhynetU Interpretation. By H. H. Turoer, D.Sc., F3^ 
Savilian Profes8or. 

Svftuiiary. 

§ I. Reference (o previous analysis of light-curree of long-period 
Tarinlilefi, anr) ctaimitiraUon hy A, the roofHcieiit of sin 49 in t 
h&ruiiinic analysis, counting B frou maximum. 

^ 3-6. Inclusiuii iu tLe series uf 13 cur\'es determined by Mi 
3. A. Purkhuivt, and forumtiou of a sot of soveo typical liKht-curre*- 

g 7-I3- TliQ niiixiitium calculated from tlie harmonic analyns 
does not agree with that assigned by ihf. nlvMrver. Is the latto 
systematically wrong, owing to the fact that the method com 
adopted of biiKctiiig chords is really no ;;uidol 

S 14-17. General skoUsh of physical hypotheais. If the 
tiou in Jixbt is due to faculae or tioccnli which arise iu 
latitudes and approach the e^juat^ir throughout most of the period, 
and then rather suddenly return to high latitudes, the aspect 
presented by the atur would modify the iigbt-currc, owing to the 
greater Importance of the faciilie ni^ar the centre of the disc. If 
one of the star's polc^s were towards the ijhserver, the faculie In 
high latitudes would be most ohrioua, the equatorial faculs beia^ 
subject to foreshortening and absorption. The niioimum w«mM 
then follow the maxlumiii early. Conversely, if the star's equator 
were towards u9, it woulil be late. 

1^ i8-2i. Coiifiiditration of the actual case of the Suo. which 
does not give safcigfactory results. 

§§ 33-94.. Reasons why the case of the stars may be entirtl; 
different from that of the Sun, owing to the smallneea of tlw 
Tariation in the latter case. 

§S 25-29. Investigatlou of the aretage factor for fotesfaortemtig 
for different aspects of the star, 

g 30-33. Inquiry whether foreshortening alone can explain the 
range in type of light-curves. The mean latitude of the facnlc 
must apparently change from nearly 80' to about 5*, which seems 
too large a range. 

^ 34 35' t^ ^^ ^^^ ^^* etfect of absorption near the limb, thm 
limits will be reduced. In default of any infoimation as to tfat 
amount of such absorption, we can neither affirm nor deny the 
adequacy of the liypothesia. But a factor cos'^' for the combined 
effect of absorption and foreshortening, instead of cos { for 
foreshortening alone (where {[ is the distance from the centre of 
the visible disc), would he quite sufhcient to make the range is 
latitude comparable with that on the Sun. 

B 3<^-37- CoUectiou of data given by Chandler for M — hi, lb« 



Mar. 1 907. Lony-ptruid Variable Stars. 



333 



I 
I 

I 



interra) betwe&n a maximum and the preceding ininttnum, and 
comparison with the dtita from ci>m[flete light-ciirreit ; labuliitioa of 
catme iieiir Ibu uuiIh of the sencK, which on the above hypothesis 
should n-'prosent «tara wltii (a) their jiolen turno<t approximately 
towards us, and (ft) witli their equators turned towards ua. 

§ 3S. Remark that while c\a,^ (b) occur in all galactic latitudes, 
class (a) aio absmit from the galactic poleg. Tliifl HU^geatA that 
tlie axuM of long>[)eriod variabloH are roughly parallel to the galaxy. 

§ 39. Recapitulation of the chief points of the hypotLesiB, and 
remarks on a [imitation not l>erL>re noticed. 

^ 40-42, Brief coueideratii^n of possible inversions of the 

hypotlifiiB. 

{a) If the faculio quite die out at minimum. 

(b) If the dark s[>ots and not the briglit faculie are the maiD 
Buurce of variation. 

Neither of these scorns so suitable an the original hypothesis. 

§ 43. Chandlm-'s periodic termn ciannot bfl due to a periodic 
change in a.^pect of the t^tar. Possibly they may arise from the 
coexistence of fieveral peri ndici ties which vary la amplitude, as 
Scbasiter has found for the Sun. 



1. In Memoirs H.A.S.f vol. Iv. p. xcvlii (or see alw Monthly 
Noiires, vol. Ixtv, p. 547], the mean Light-curves for 19 long- 
period variables obeerved at the Rousdon Obeervutory iu the years 
18S5-1900 are reduced to the same scale of period ami of range in 
magnitude, and analyAed harmonically so ad to be doeely repre- 
Koted by the formula 

M-t-Asin tf+Bcos d + Csin 2^-f-Dcos 2tf+EBin 30+Fcoa 3^ 

When the resultit are arranged according to the values of th« 
coefficient A, the other cuefficientA an found to be in approximate 
sequence also. 

2. When Mr Parkhnrst's " Researoltes in Stellar Photometry, 
1S94-1906,"* was received, containing iz new light ctirves, from 
observations made chiefly at the Verkes Observatory, it was natural 
to exBuuDe whethiT Ids curves fell intu the ttame sequence, and the 
answer was sulticiently satisfactory. lie has indicated in each 
cua the ep<}ch of maximum, and given diagrams of the smooth 
curve*. From tliese curves reailinga were taken at twelve eo 
distant points, beginning with his ussigued maximum- Theiv 
were then analysed harnionically, just as in the case of the B' 
Tariables, and the results are given in the following U 

second decimal place must not be regarded too serioii' 
the reason that it is not always easy to make precltt 
the curves, owing to the steep gradients which so 

* Otntegw Institntioa, October 190 



334 ^'"o/ -ff- -ff- Turner, On tht Clauijieation of LXViL 5, 

Table I. 
(OorTMponding to Tftbl* UV.. J/mu R.A.S., \v. pu xdx.) 



Kftiur *- 


nanaHn 
Kumtxr. 


«A 


6B 


«c 


6D 


«R 


«F 


IVxnst. 




S Oygni 


7220 


+0*24 


-4*83 


-•'5 


+ ■02 


■13 


-*ai 


IO'2 


4^ 


W Androni. 


787 


-0*36 


-3'04 


-•11 


-•40 


+ 107 


-'09 


7*5 


rs 


R Hercalu 


S79S 


-0-54 


-153 


-•29 


-■34 


-'34 


-■36 


S-5 


$1 


RConue 


431 S 


-0*64 


-284 


+ '30 


56 


t'oB 


+ •02 


88 


4^9 


VCuaiop. 


S639 


-0-90 


-373 


-XI9 


-v> 


+ •16 


-•28 


97 


4*B 


V Androni. 


267 


-0-91 


-a-«7 


+ •2$ 


-14 


-'IS 


-•12 


9*3 


4*a 


R V Horculi* 


6100 


-1-04 


-1-73 


+ •53 


-■03 


■foS 


-x>8 


lo-s 


r* 


S Lyra 


6894 


- Via 


-2-55 


+ -&4 


-■28 


+ «2 


+ •13 


lor* 


«TS 


T Aiidroiu. 


103 


- I'll 


-173 


-■02 


-•3» 


+ ■02 


-•16 


8-s 


4-3 


[The Sun] 




-1-49 


-2-32 


+ *II 


-•70 


■(-•19 


-19 


... 


— 


V Dcl|)biiii 


7458 


-l'54 


-1-24 


+ ■06 


-■64 


+ 104 


-■16 


97 


r» 


S X Cygoi 


7269 


-1-57 


^258 


-•14 


-"30 


-•02 


-•36 


9-1 


4-» 


Z Cueiop. 


S51S 


-rSo 


-a-i8 


+ •04 


-•54 


-•02 


-•JO 


^o% 


4iJ 






3. lu tbe series have been inchuleil the valuer obtained for Uu) 
Sun {Monthly Noti'-ei, Ixiv. p. 549) on the bjpoTheeifi that Wolf* 
ftpcit numbers can be Lakeu as an indication of lightrvariabilitT. 
The spota theiiiHslvcs would imply loss of lif;ht ; hut this i« 
probably more ihan coiopeusitteil by the inoreased brilliauoe in tb« 
accom[iuD,viiig foculte or tloccmli. It is not tin reason able lo 
compare BpotteitneaB directly with th« lightrcnrves, for the stelW 
magnitude of the Sun would be proportional to 

-o-4iog(P + F) 

where P is the brightness of the ordinary disc, and F tba 

iacrcmeut due to facuhu which may be taken as tongbljr pro- 
portional to the obeerred spottednesB. , 

Now log{P + K) = logP + log(l + F/P) ■ 

= log P + fcF approximately ^* 

whent A: ia a oitnstant. Thus F appears in a form appropriate for 
compariHon witli E<ti:lbir maguitndes, since >u all rjvses we aabtrut 
a ooufatant (correfi[>oniling to log P in thi-t case) and dividfl by a 
factor (the factor k). The peculiarity '»f the Sun is that the 
sabtracled constant is so large. This makes no ditference at 
present, but it is important lati>r (tj§ 22-24). 

4. A point calling for 8|%cial remark is that the Sun is n 
included in the S6ri<« iontead of being outside it aa befora. 
extreme value of A fur the Rousdon variables was - 1-26 ; 1 
Mr I'arkhitrsl's t<eries cuntaltis three stars with negative values 
A greater than this numerically. There is thus no longer 
need to extrapolole for the Sun. 

To show the accordance between the former seriee and that 
provided by Mr Parkhurst, the values of ii, B, C» etc, for the 
Kousdon vaTiab\eain\fi,'U^WvaV«(iiut«v^ted along with the abovs 




1 Mar. 1907. 


Long-period VariabU Stan. 






335 1 


H Tatties in Ttible I. 


Butil 


was 


CO ruddered 


a better plan to 


go 


back ■ 


H to tbe liglit-curvus 


auJ (<ive 


tllQ 


artuat 


reaJinua for the twelre ^H 


standttcd poinrs, as 


ill 


'U 


lie 


11. 


The KouAiloa curves are simply ^| 


re|»roducf»l from Table LIII. of p. 


xcviii, 


Mem. It.A.S., vol. Iv. ^^M 










T&BLK II. 










^^H 




Liyht-Carvfs aecntrtimj to Value 0/ A. 






^^H 


Name. 


6A )lax. 


2 


3 


4 


5 


6 


7 8 9 


10 


11 


^H 


T Oaosiop. 


+ I-S3 





16 


40 


63 


91 


99 


78 48 33 


3a 


*4 


^H 


T C«phei 


+0-75 





16 


39 


63 


87 


102 


98 78 S» 


38 


34 


^H 


S HerculU 


+ 50 


a 


10 


32 


S4 


S4 


99 


94 76 60 


47 


23 


^1 


SRoAtii 


+ -46 





7 


33 


47 


76 


9* 


100 87 57 


3» 


M 


^^1 


R Auri^ 


+ 38 


a 


'3 


33 


57 


7S 


96 


I 01 79 53 


44 


39 


^1 


S Urs. Maj. 


+ '35 





6 


19 


44 


67 


85 


98 86 S3 


35 


M 


fl 


SCj-gni 


+ -34 





14 


3> 


56 


77 


94 


too 93 65 


43 


31 


la P ■ 


E Lyiicia 


+ -07 





8 


36 


45 


66 


87 


100 90 62 


39 


27 


1 


B Uauelo]), 


+ -07 





6 


24 


46 


66 


86 


lOD 88 66 


40 


21 


1 


S Ophei 


'00 





9 


27 


5' 


75 


93 


9S 86 64 


57 


35 


^H 


K BDnco. 


_ -08 





7 


27 


49 


75 


93 


101 97 80 


54 


24 


H 


I xCy^t 


- '31 





9 


36 


48 


68 


87 


100 100 80 


57 


33 


1 


H W Antlrora. 


- -36 





10 


*9 


56 


So 


95 


too 9S 85 


71 


45 


13 F ■ 


H R U HnrculU 


- '54 





9 


32 


60 


74 


87 


98 100 79 


66 


58 


3<' P H 


H fiCsBsiop. 


- -63 





10 


2S 


45 


66 


87 


97 97 87 


65 


44 


1 


H ROiitue 


- -64 





6 


37 


53 


69 


83 


92 too 9S 


8* 


47 


to P ^^1 


W BCygni 


- 77 





It 


36 


42 


57 


73 


92 102 92 


64 


38 


^^^1 


T Vn. M^. 


- -So 





S 


21 


41 


61 


77 


93 '°' 94 


69 


3S 


H 


TDnoo. 


- -88 





8 


31 


38 


54 


7< 


87 98 89 


65 


38 


^1 


Y Ou«io{i. 


- -90 





li 


3S 


63 


78 


90 


98 100 100 


92 


73 


18 [' H 


V Androm. 


- 91 





5 


31 


38 


55 


74 


93 100 88 


64 


40 


17 ■ 


R V ]hK%ih» 


-|<H 





8 


18 


38 


46 


6y 


93 100 90 


67 


}> 


■ 


8 Lyre 


- no 





7 


zo 


31 


46 


63 


8t 96 100 


65 


33 


7P ^^ 


T Aadrum, 


- rii 





7 


31 


44 


63 


84 


98 100 96 


79 




" ^^^H 


R Vn. Mftj. 


- I'll 





8 


31 


39 


59 


78 


93 iQo 9i 


r 




^^1 


SCorouiH 


-'■'S 





5 


17 


32 


47 


62 


77 9J ttr 






^^H 


R Caaaiopi 


-1-23 





13 


30 


42 


47 


7' 


93 "» 






H 


U Oriotiis 


-I 26 





8 


24 


43 


63 


78 


93 100 






1 


[Tb» 8dd] 


-1*49 





9 


43 


3« 


54 


7> 


«4 94 






1 


V Dclpbini 


-IH 





9 


»3 


37 


54 


69 


83 9* 








SXCygni 


-l*S7 





5 


»7 


31 


50 


79 


95 '0 








ZCunop. 


-rSo 





8 


21 


33 


48 


67 




H 


m 


^^ 



336 Prof. II. M. Turner^ On tht Classijlcation of umt 5. 

The unit for ilic table is o'oi, in order to avoid ttie a»e ol 
decimal points. The curves iltie tu Mr Parkhuret are indicated t'j' 
the letter P in the last colnmn. 

5. Oliincing dovrn the columns, there are considerable irregular 
itic^ which may be toe Kteat to be ignored ; but the aocidtntal 
errors of light- estimations are targe, errors of half a magnitude 
being far from imposftiUe. [The average range in magnitmle of 
these variables is about 4 ; and 05/4 = -13; bo that half a mftgm- 
tude means 1 3 units in thw table.] 

If we Dia^' regard the emtrs as chiefly accidental, we may Qstimatt 
mean valuer by grouping the slurs aa follows : — 



Table III. 
JCHimattd At-^ian Ordinides/or Sttfen Orvupe. 



Oronp. 6A. 


Mu. 


z 


3 


4 


5 


6 


7 


8 


9 


10 


11 




I. +10 





13 


38 


61 


87 


100 


94 


70 


40 


30 


17 




11. +05 





12 


32 


54 


78 


97 


98 


83 


S& 


39 


26 




III. ov 





II 


28 


48 


70 


90 


too 


93 


72 


S» 


34 




IV. -0-5 





10 


36 


44 


63 


82 


98 


too 


£6 


65 


4* 




V. -i-o 





9 


H 


40 


57 


T6 


93 


lOO 


94 


77 


53 


30 


VI. -I'S 





8 


22 


36 


52 


70 


87 


98 


9& 


89 


64 


a 


VII. ao 





7 


20 


32 


48 


65 


80 


94 


99 


98 


75 


31 




6. Wemiy now submit tbe»e mean curves to analysis and obtaia 
the follo\ring coatficientK. 

Table IV. 
Ooe^ieni* <^ JffannOTitc Tnmufor Carvu (^ TahU III, 



Group. 


6A 


6B 


6C 


60 


6E 


6F 


6A4 


6Bj 


I. 


+ 1*07 


-257 


-0-46 


+ 0-0S 


+ 0*02 


-O'M 


-O'OI 


+ o'i* 


II. 


-I- 0*46 


-262 


-0-25 


+ 0'I0 


0*00 


-0-32 


+0'03 


+ 0-07 


111. 


-0*12 


-279 


-002 


O'DO 


O'OO 


-0*30 


+ OXtt 


+ 0-04 


IT. 


-0-66 


-275 


+ 0-I8 


-o'i6 


O'OO 


-0-I7 


+ ox)7 


-f-o^ 


V. 


- ri2 


-258 


+ 0'i8 


-0*36 


+ 0-03 


-019 


+0-05 


•f-o'06 


VI. 


-^■$1 


-233 


+ 0-H 


-054 


+ 005 


-0-23 


■t-o^ 


■f ooS 


VIL 


-1-88 


-2 '05 


-o-os 


-0-69 


+ 006 


-038 


•4-0*04 


+0-13 



The coefficients Qf the fourth liarmoiiic, A, sin 4^+ B^ ©oa 4^, 
have also bei^n calculated as a general check. By retaining the 
fuctor 6 (which occiitk in the arithmetic), the range in nia}{nitu<ie i> 
represented ad 6, a larger range than nsually oocura. Uouca the 
fourth harmonic ?tt;ldom makes a difference aa large a« o>i 
magnitude, and we may not uuruosonably neglect it 

7. A curious point now arises. The angle B in the expression 



^ = A6in d + B Goae-vCaVtt sQ-vW cwid+Esin 3^ + Foo«39 




Mar. 1907. Long-period Variable Stars 



337 



has been reckoned from a maximum, and hence we should bave y 
a maximum when 6=0 ; llie condition fnr vhicli is 

A + aC + 3E=o 

Bat this condition is not fulfilled : id group VII^ for instance, 
we have 

6(A + aC + 3E)= - i-88-o-io + oi8= -i-8o 

Tt wan at Hrst siipjiosi^d that tbera vtak some mistake tn 
calculation ; and to test this, the curve was recalculated (C) from 
its furmul», ijxcludiiig the funrtli Irarmonic, lor oomparison with the 
asaumed 12 oriiiniites (<)) as b«]ow 

Max. (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (i») 
(C) 3 4 22 34 45 66 84 94 98 99 77 35 
(O) o 7 20 32 48 65 80 94 99 98 75 38 

(<?-<■) -i +3 -2 -- +3 -' -4 0+1 -I -2 +3 

There seems no reason tu duubt the compututiona ; but the 
obaerved and computed curves clearly do not tit closely at 
maiimum. Tliey intereert thr«e times, anil it would requira a 
harmonic of a higb order to obtain a }{ood lit. 

8. There is nu rea.s<iii why there should not be a harmonic of a 
high onler : but neither is there any good Kssoa why there should 
be. The nece-saity fur it may be avoided by a simpls supposition, 
but aa yet wo cannot say whether that supposition ia true or false; 

F N 



^B 



<H 



Fia I. 



that can only bo determined by a much more accurate knowledge 
of the shape of ligbt-cnrves dote to maximum. The supposition is 
that observers may have made a Bystcmatlc error in assigning the 
epoch of maximum in cases where the rise and fall are not equally 
sharp. It is a cuiuuion practice to assign this epoch by drawing 
(he curve which bisects the chords joining equal magnitudes on tbo 
rise and fall ; and it is now Huhmitted that this practice cannot be 
defended, and may even be quits wrong. Tiie reaifon will be clear 
from the above diaRrami. 



338 Prof. H. B. Turner, On tiu ClaaaificalioK of LXVa 5. 

lu Gg, I ia a portioa of a [larabola toaching RMS at the poioi 
M. The looua of the middle poiats of (janiUul chunU sucii u A B 
is, an WA know, the sti-aight lino LM cutting the curve at Uu 
required point M. But it is quila easy to draw a carve, sa in 
fig. 2, wliurc the lociitt uf tbese middle puiotit is a curved tine K X . 
and wliere the portion V K prudacej wuuld carry us towardi 
point F HWity from the itno maxinmiu. To re^iliso Ibiis wu hal 
only to supjwsL' tin: cui'vo V K N druwh iirst along with ooe 
Cl^Nof ihw curve. Wo can then constract the utiitfr side 
producing; G K and similar lines to equal difttiinces on the otl 
side of V K N, whvn wv shall g-.-t a smooth curve N H T). 

y. \Vu might havi? drawn V KX N much more cur^'cd, mnd stiQ 
it might be made a Iociik of midtile points of chords. The azga- 
ment ttt of some impurtuncc, uiid may )>» pnt into an analytical form 
for comparison with our formula-. We have ndopteii the formuli 

y = A sic 9 -(- B coa 9 -f C ain 3 tf + D cos 36 + E fiin 3d -t- F COB 3^ 
and near 0-o this may be put into the form 

-i{A + fiC + 3 7E)tf* + eta 

If the origin Lb a (>uiuc of maximum, the constant la » 
further 

A + iC + jE-o. 

Thos the curve near the orig^in takes the form 

y = W>-o^ .... 

where a- J(A + 8C + a7K) = C + 4E 

in virtue of the relation (3). 

We may put this in the alternative form 

which hofl the advantage of giving^ only two values uf $ for any 
assigned value uf y, exiliiding a third value of 6 given by equatioe 
{4), at a 6nitie distance from the origin and irrelevant. Hovt 
these two values of 0he 9, and $j, the co-ordinates of the mid 
[joint of the chord joining them are (x, y), where 



X = 1(01 + 6^ = ay :ifl 




1 



and the equation to the locus of middle points of chords Dear thi 
origin is thus 

6» (B + 4D + 9F+ . . ■)« • 

y"n" 4G+4E+ . . . .)-^ ■ 



[Sriar. 1907. Long-period Vitriabk iitars. 



339 



If there were only the lirat harmonic, all the cw](Tl<.'ienttt C, D, £, F 
[exctipt A and B would Iw zito, and the coefficieut of x in 
lequatioD (S) would W intinice, so tbnt the locus of iiiiddlo points 
^vonld cut the axis of :i; at right angW If wc take in the next 

harmonic, then »ince C and l> are Hmall conijMired ivilh B, the co- 

efhciuut of x is still very latj^t, and tho direction of the loci\a is 
ifiearltj at right augleu. But when we take in K and F, 
[ftnd mmv and more as wo tuko hi hurmouics of hi^'h^r ordor, 
jihey are mtiltipticd by factors which increase rapidly and in- 
sdefinitfly; m tliat t\nii xij^m and the niagnitnde nf the coefficient 
[of X in cifuation (8) are ultimiitoly controlled entirtly by harnionics 
|of a high order, however small thuir coelEcieiits may l»o. We 
L«anDDt tbwrefore assert OJfythinfj abotit the oltimate direction of the 
[]dcu^ unle^ut we kiti>w fmin i[idHj>i^ndent connidarAtiona what ia the 
laracter of these Imrmonlca of hi^'h order. Tbe locus of middle 

)oint8 is not exiicily u b^d ^uide to tlie muxltiniiii (or miuimuni); 

It is simply no guide nt all. The epochs shuuld not. be H.<«sigii6d in 
lis wav ; * and if they have been so assigned in th^ pust, they nmy 

be systeinaticAlly wrong. 

10. L'n the oth^ir hand, there iii no way of ascertainin); the error 
[except by closer and more continued observations near maximum. 
[The amount of i-faslblw error may be illu8trat.;d by determining 
[tlie maxima in another way, viz. from the assumed formulw. It 
tU at least ecjtially good (or bitd) with the former, and a companion 
[of the two tuethcKls will show the kind of error to wluck either is 
[liable. 

ri. It will suffice to give an approximate correction. In the 

nelghbourliood of ihe origin wt- have 

Let ^ be a maximum when B^t, Then 

a — /?€ = O 

The values of a, ^, and e are given below in Table V. The 

[deduced values of c do not tit in very well with the hypotliesis of 

ta syslemutic (frror in estimating, for they an not symmetrical ou 

■ Opposite sides of group III. ; in other words it grei<:ter t;rror is made 

when the rise is sharp than when the full i8sbar|>, the reason for which 

is not appurttnt. But the plif^ni)menr>n is of a progressive nature. 

Further con*yerstion has \rA to tin- view thnt tim cliftrncteristii^a of tb« 
irvM mii&t l>e dtilKitiiiiiRil in a totslly ilitfcroiit way, tiy caK-ii luting nivu 
1(1 ccDtm of gnivity and momt-Dn. But tliie dieiTUstnoD itrfserT«d for* 
^ftxture paper. 




340 Prof. H. H, Turner, On the Clauificatian. of LXra. J 

Table V. 
CtUetUation <if ComdioH to S}jock of Marimum. 
6B Ratio. • 

-4'20 

-4"59 
-492 

-573 
-656 
-Sa3 
-683 

12. Wlifn we alt^r the epiK:]i of maximum hy c, the t«rms to a' 
are altered by 2c iind tbose in 3$ \iy 3c. Tbe new vatuea of Uiecfr 
eHicicnts are given in Talile VI., which, od the hjpothoaia not 
luade, ithould re|)lace Table 1 V. The oM value of 6 A im iDscrtvd it 

the second column to show the change. 

Table VI. 
Cometal CotfieiatU t^tke ffarm*mie Ttruu. 



Group. 


6* 


I, 


+ 0-2I 


11. 


-0*04 


ni. 


-o'i6 


IV. 


-Q-JO 


V. 


-070 


VI. 


-I-I6 


Til. 


-|-8a 


The Siiu 


-0-68 



-0*030 


-JI9 


+0*009 


+ 05 


+ 0*035 


+ a« 


+o'o6i 


+3*5 


■fO'lZZ 


+ 7*0 


+0177 


+ 10*1 


+0*219 


+ 12-5 


+ 0'IOD 


+ 57 



Qronp 


6A 


6A, 


6B. 


6C, 


6D, 


6E, 


6P4 


I. 


(+1-07J 


+ 0*96 


-2-62 


-o'45 


+0*13 


-o-oi 


-©•a 


IL 


< + o-46) 


+ 0*49 


-2-62 


-025 


+0-09 


+ 0'0t 


-0'2> 


iir. 


(-0-I2) 


-OOJ 


-279 


-OX>2 


ovo 


+ 0-02 


'OIO 


IV. 


(-0-66) 


-o'49 


-279 


+ 0'20 


-o'u 


+0-03 


-0*17 


V. 


t-i-ia) 


-0-80 


-2-69 


+ 0'26 


-0-31 


+0-08 


-017 


VL 


(-1-53) 


-1-09 


-a'57 


+0-3S 


-0-47 


+ 0-I6 


-o'i7 


The Sao 


(-»-49] 


-1-25 


-»'44 


+o'a4 


-071 


+0-95 


-o'i3 


VIL 


(-1-88) 


-139 


-241 


+028 


-0"64 


+ 0-38 


-0-26 



i 



13. What is tme of ttie groupd i^ of course, true of tho dete>- 
minatiunn for individmil Htars ; and if we return to Table TI. aad 
calculate the ejiocba of niaxitnutn from the cooflicietits giran it 
Tiilde I. (ur fur the Kmiadon stars in Memoir* JLA.S.t vol. If. 
ji. xcix), we shall find different values for A. Tbuse which folio* 
the general law aljove notict^d call for no further remark ; but thai 
are some which go thu other w&y, w that ihoir places ia the serin 
are cou»id).TBhIv cliaiigwl, The must notable cases are — 



S U're. U^. 


+ io' 


Old A 

+ 0-35 


Now A, 

+ o*K4 


K U Heronlu 


+ 17' 


-0*54 


+0-30 


R V UflreoUi 


- 4" 


-IXH 


-tZ4 


S L^ne 


- 5" 


-no 


-'•37 


R Vn. MiHJ. 


- 5' 


- rii 


-r3« 


S Coron« 


-lo* 


-IIS 


-I-66 



Mar. 1907. 



Long-penod Variahle Stars. 



341 



It wflft founit, however, tlxat nothing ftsnentiallf haw was added 
by making the individual corrections ; und aa it is by no naeatus 
certain that they are justifiable, tlie corrected table ue«d not be 
given. 

14. The qiioistinn now arisfljt — Is th«re any pbyaical reason for 
this gradation or sequence in the light-curvea 1 TKe fact* suggeet 
a light-curve uf watntially uniform ty|ic, modified by sonic wcondary 

;caiue. The place of tiic Sun in the series suggeslH the consideration 
of Bokr pbenuniens as a poij^Hibb type for all these varlablca. Is 
there, tbeii, any way in which these phenomena would be slightly 
modihed in the cane of ntatK scattt^red at random t 

15. One such Bonrce of moditiiaition is curiaitily the difference in 
[lOfpee/. We view the Suu from tlie direction of hia trquator, 
I whereas the stan niujft present all ospocts to us from ]>ole to 
[equator. What wonld Imppen to the .Sun's light-curve (as repr*- 
[aented by the spot-curve) if we viewed the Sun from the direction 

! of one of It^ poles 1 

i6. Tlio ^'oneral consequence is easily seen. Spots in high lati- 
tudes would always b<( m^ar tho centre of the apparent disc, while 

, those near the equator would be considerably fores hortenu*d. [The 

' same would be the case with faculie : it need not ciiu»e any mia- 
vnder» landing if wu speak of Uiu marc laiuiliar spots throughout.] 
They would also suft'fr absorption near tbe Iluih ; but for the present 
we will omit this fact, and think only of the foreshortening. 

Iti^ginning with the epoch of niaximum, the snhsequent spots, 

l^ing in lower latitudes, would be more foreshortened aod 
dimiulabed in value, which would wake the fall to minimum more 
rapid. Directly » fr-w small spots appeared in high latitudes, their 
enhanced value would start the rise to uiaximuiii. I!ut as the spots 
increased in number and size thuir latitude would diminish ; Uiey 
would leave the centre of the disc and become fore.<ihortened. 
Thia would to some extent compensate the increase in numb«r, 
aud render the rise to maximum less stoop. 

17. The general effect above described is exactly that which 
vould carry the Sun towards the other end of the series 4if light- 
curves. At present the fall is slow and the rise rapid ; if we 
viewed the same phenomena from the direction of the Sun's pole, 
the fall would be more rapid and the rise slower. There remain 
fche questions — What is the amount of the cliange? and how is the 
general charui:ter of the curve affection 

iS. Wu will first consider the actual case of ihe Sun, though, for 
reasons which will presently appear, it is not a satisfactory example 
of the stars. The (Ireenwich Obaorvationa give the following 
values for the "mean distance from equator of all spots" in the 
years 1883-1904, arranged m two periods of eleven years. 



342 FtoJ. n. II. T-Hmif, On the CUtssiJicaHon of Lira 

Far the smne yvaN the " ourreotail orwu " are (^ivea as follom : — ^ 

1st Cycle ilis 1079 Sit 381 179 89 78 99 569 1214 i^ftf 
M<ICyol»ii82 974 543 514 375 Ml 75 a9 62 340 4B 

Me«n . 1219 io«7 *77 -(48 277 100 77 64 316 777 tflO 

The factor for foreshorteniiij^ trh^n the spoU are supposed toll 
viewed from the pole is gin A, which is very nesu'lj proporiiantl Id 
A, and may he so talceti for the presftnt pur]»ofle. Multiplyiog Ibr 
t\ro rows of meana wo get to 3 signiticant figures, 

166 127 89 41 36 8 7 10 60 149 153 

To treat thi« as we hnve treatetl the lijrhl-curves we suhtrart 166 
and divide by 159, reversing the sijjiis so that Diojciroum b 
representeil by xero and mininiuin by + I'oo, obtaiiimy tUer^fow 

00 24 4S 79 88 99 too 98 67 XI 9 

19. To ccmpare with this we must take the ** project*^ arcw" 
ns we see tkem from the dliectiuii of the eqtiator. Aa given ut 
the Greenwich volumes fur the «iiin^ yenrs these ara 

lit Cycle I59S 1478 1122 527 243 125 103 in 745 1596 19SJ 
20(1 Cyclu 1728 1330 745 695 532 159 toi 4t 86 434 65; 

Ucau . 1662 14a; 935 fill 38:1 142 102 87 416 1015 i}il 

and treatiog these in the sanio way we j^et (after subtracting t66: 

and tlividing by 1575) 

o 16 46 67 Si 96 99 1 00 79 41 22 

20. There are only eleven terms in cnch case instca*! of twetra 
We might draw ft curve and rwid off twelve point« for aoalyiJi 
as before ; but it seeuu better to tuke actual obeervAtions voi- 
touched, and the iibove numbers have been analysed 00 tlv 
asstini(iiioii llmt the period is exactly eleven years. The rasaiUin 
as below : — 

GA 6B 6C 6D GE 6F 

From Pole. . +050 -306 +0-53 -0*26 -0-14 +o*«S 
From Kc)UAtor . -0-28 -3*82 +0*24 -0*47 -d'io -0x14 

II, Th«re is thus a change of sign in A, and at first stgkt it 
would appear that we have obtain<^d an effect of tbo kind reqaimL 
But no Htt«iiipt wiui mude to aJjsi^n the iiiaximum accurately^ ud 
this is still to bo tlonn by the methoti given above, the valiKM «j 
A + 2C-f 3K being ditferatit from zero in both cases. The tkIm 
for the second curve is small, and we find «= + i'"a. For lb* 
(irat, A-f2C + 3E \a so la^^l.' that the approximate mf^tho^l \m 
finding c will not work, and we must liud it by trial. The vilw 
c—z?* is near the truth; and on substituting it the value of &A 
is changed from + 030 to - 0*95, which ison thn itther tide of ll)* 



.Mar. 1907. Long-period Vai^ahU Stars, 



343 



value for equator view. Indee<I & miigli sketch of the two curves 
without any aiialyais shows thai Chcy are not very diRbraut iu 
typo; and thnc alth^m^h t!ie npot miniiiitim of tho ciirv« has 
bMn shifted, tho uiaximum has been shifted even more in the 
same direction; so tliut thu curvi.', instead of being clanged from 
a "late" to 111] "eariy" typ«, :s "later" than ever. Tlie fact ia 
that the poculi.iriiy nf the Sun already referred to in ^ 3 makes it 
for this purpose an unsuitable representative of variable stars. 

3 2. 1^1 iiscoiisid*^r what arc the conditions determiuing the ehif t 
of a maximum or minimum. Ln the neighbourhood of such a 
point, for which ^= 6^ ^''T* *^^* nrdinates are of the form 

y, = K(tf - B^Y + higher powers 

[If to theee we add ordinates of the form 

y, = G(fl-e„)+ 

we shilX the position of the maximum nr minimnm. The condition 
for His 

and the ahift is thus G/sK provided G is small compared with K. 
The quantity O is the gradient of the second curve, and K 
repreBenis the curvature cf the lirxt. Tlie sliift can be increased 
then by increa5ing the gradient of the second curve, or by 
dtminiwrn^ ihu curvature of the first. Finally, if curvature and 
gradient be both reversed iu direction, the shift remains unaltered 
in direction. 

33. To apply this to the example jii.st given, we musE tirst take 
logarithms of the <)uantiiies used in order tu substitute the addition 
of two ordinates for their nmltipliialion. Let 8 lie the sjMtttfd 
area and X the spnt latituJe : we formed the prodnct 

Taking logarithms wo get 

y = log j:«log8 + IogX=y,+y3 say 

and we are concerned with the alteration of the maxima and 
miaima of y^ )>y the ;^radient of y^. Now the gradient nf y is 
small near a maximum of ;/,, but sharp near a minimum, when 
Uie spots quickly cruss into high latitudea. TliUs in ^ iS we aeo 
that th() mean latitude changes near minimum from 9 '7 to ig*'o 
in two years, the change in the reTento directioti requiring se^en 
or eight years. The gradient at minimum being thus much 
sharper, we might ex{>ect the shift of the niiuimum to be much 
greater than that of the maximum -, and in the case of the stars 
we Kh&II presently see that thid probably happens. Hut in the 
particular case of the Sun the sharjier gradient in y, is more than, 
compensated by the greater curvature in t/^. T\\l& atxa tvqX i&^^iu 



344 ^^9f' ^' H. Tiiiiter, On the ClassyUcUian of 



urralll 



iu the spot numbers tbemeolTes ; but wlieu we take logsriUimi •# 
get tbe following quantities, omitting a conetant, viz. — 

i'3i i'23 i'05 o'&i 0*67 o*ai o'la '03 0*73 i*i 1 i"3i 

which represent a curve wjlh a curvature at minimuni mod 
shtrper than at maximum, which in not the c-ase with Ik 
mftgnitude curves of long • period variables. This diffemm 
hetvoen the !5un and the stATA is important for our puri>ose. Il 
is the 8i)n-fl])0t nnrabors themselves, nnd not their logarithms, Ihit 
resemble the magnitude curvea of variables ; and it was remarkri 
above (|i 3) that they provide the proper analogy when tat 
variation in brightness is small. 

24. Anoih«r way of regarding the matter is to think of actual 
liri^htnesa curves for the stars. A rise of 5 maKnitude^ far 
instance, means that the brightness at raaximiim is too times ilul 
at minimnm. If we drew the curve with tbe ordinat« at maximoB 
5 inches high, the ordinatea near minimum would be very small 
The curve would be very Hat near mitiinium, and shoot up into a 
Buddeti Ui^'h \tvsk near ruaxiuiuui with, of cuursc, a sharp curvaturr. 
For llio Sun this high peak is evanescent ; or, if we magnify il lo 
make it noticeable, the zero line of our light<:urve re<^as lo s 
very groat distance. 

35. In conHidcriiig the effects of foreshortening for tbe stan, 
we may deal with either the light-curves or the magnitudr-canm 
Ici the furmer case wt) multiply tbe ordinates by factors: io the 
latter we add other ordinatea to them, representing the loganthoM 
ctf the factors, tint we must remember in either case that it ■ 
the faculje only which are eupposod foroehurtened. Lei P be thi 
total lirinbiaess of the photnsphere, F of tbe faculu^, and B of thi 
two together, and iet « be tbe factor for foreshortening. 

B-sF + P 



>I IBS 

1 



If we have two different aspects of the star for which the rolua 
of 9 are s, and «j, respectively, then 

log B, - Ing B, = log (*iF + P) - log («,F + P) 

Now, near maximum P is verj- small comparwi with »F, and we 
may neglect it. Thus 

log Bi - log Bj = logs, -logs, 

26. Consider now the case of minimum. If the facnUe 
altogether, so that F = o, then 

logB,-log lV, = o 

Tlie minimum for both eases is then the same, aa is 
obvious. 

If tbe focule do not entirely die out, 

log Bi - log Bj = log (iTj +p) - log (sj + p) 



[ar. 1907. Long-period VanahU Stars. 345 

rhcre p u writtou for P/F, ami U poBitive. This difference is 
Jwajs less tlmn Log k^ ~ log n^, bat approaches it as p diminiahae, 
'.,8, as the faciilsB at minimtim aro brighter compared with the 
photosphere. It is nut hy any mcaas impossible that if the 
JmmeuHe iucioase iu bnliiaucy of ihi-se start) is diie to faculie, 
ihec even at miuiiiium there may be faculie whose brightness 
"irgely exceeds that of the photdspliere, so that wc might write 
pithout sensible error 

log Bj - log Bj=- log 8, - log s, 

throughout the whole light curve. For einipHeity we shall 
[consider this caae firitt : tlie requisite modi tica lion for otlirr caees 

Cau bo considered later (§ 40). lUit we may again remark bow 
J the case of the >Sun ditTers from that of the tttars. For the Suu 
[p is ttlways a large quantity even tit maximuni ; and a different 
fformula is appropriatfl, viz. — 

27. We must now consider the factor s. When the Sun's or 
'star's axis is tilted, tho visibility of a spot ift atfectfd in two ways. 

(a.) Le7i(]ih 0/ visible ftatb. — If the pole is towards us we see 
I the whole piith of a circum|>olar spot ; if the equator is towards us, 
'Only half of it. But If the spots are symmetrically distributed in 
both hemispheres, thi-n^ taking a pair of equal latitudes together, 
we always t^ee just half the length of path of t1ie spots in them. 
"When a pole is towards us, we see the whole path in ime 
hemisphere, none in the other ; when the equator is towards us, 
we see just half of each. Hence the mean length of vi»tble path 
is not altered by tilt of the axis. 

(6.) Fore$kortfninrf. — Let K be tlie latitude of a spot, t the 

distance of the pole (P) of the star from thfi centre of the disc 

(Z, tig. 3). Then, denoting the angle SPH by Z, the angular 

' distance { of the spot S from the centre of the disc Z in given by 

cos { = cos « sin A. + sin « cos A cos Z. The foreshortening factor 

I is just this liOR {, and the mean factor for the spot may be taken a^ 

/* cos { f/Z c^ [Z cos « sin X -f sin < cos A sin Z] 

' the expression in brackiits being taken within limits, say from - a 
to + a. Now if we take a pair of latitudes ( + A and - A) together, 
the limits for -A will be -(»•-&) to +(Tr-a); and ths total 
effectiveness will thus be 



« a 3( 2a - ir) cos < siu A 

I a being given by the equation 

cos a*a - 

It will be more convenient to pa 
1 Hie eqtutior- ' '»me 



Xatn 



tue tlie angle (3, 



346 Frof. H. H. Turner ^ Chi the Claesifieation p/ ucto. 5, 
aiid < = 4^ CM c, sin A + 4 C4)S /3 sin c cos A 



in which j9 is to be put equal to ^ for all ralues of X greater thin * 

3 



D 


((/^\~ 


1^ 







1 



Flo. 3. 



38. Tlie extromo caaee are simple \— 

Kquatoriai View. Here t = 90', ^ -= o', and 
« = 4 Ct.>a A. 
1og«siog4 + Iog coeX 

"Rie log 4 may be iliii^rcgardtid ah u eoiisbiDt addition to thetirtt- 
curve. Th^ term log cos A can theoreticnll; bavi> any T^ue fno 
o to - 00 ; but A in practiw is to be tnken a« a n»-?rtn latitude, ud 
is not likely to eicced (say) 70" ; for which lop cos A= 9'53. "Htt 
range in lo;]; 9 ia tbua not more tban 05. ^'ot« that in tbia cast 
log 8 decrease$ as A ina-eofe*. 




Polar View. Here «=o', j3«»9o', and 

S'=2ir fiin A 
log* = log }ir-f loggin A 

Tbe miige in log ain A is again theoretically infinite ; but the vmm 
latitude of tbe sputa is not likely to approach nearer the eqaxtot 
than Bay 5*, for which log sin A = 8-94. The range in log » ii 
therefore litlk greatet V\\Mi uiiStej^ wa4.\l increoftM ae A increaiMi 



i 



I Mar. 1907. Lo7tff-per%od Varu^Ue Stars. 347 

39. Interm&iiate Casea, For other values of « the formula U 
I more complex, but the change in log « u intermediate belweeu the 
; above extreme cases. The general character of it can lie readily 

I seen as f oUowa : — 

Put ^ cot y i= tan c COB ^ 
then « = 4 cos «. j8 costc y. coa (X - y) 
When A - o, /9 = o and y = o 

When X ie siuall 
y?eXcotc, y=Xcot^€, « « 4 ain e COS AA, where A: = cot^<-i 

And when X = t,/3:= -and v= - 

2 2 

I and the«p latter valties of ^ and y are to be retained for all values 
of \ gri^ater than t. 

Hence when X is near 90^ 

8= ST COB c sin X 

The caie when 4 = 4,5* ^^^ perhajts sufficiently illustrate the nature 
of tho variation in log «. The values of fi and y aro (fivcu below 
jn degrees, but thi» need cause no tuiffiitnleratanduig. 



Tablk VIII. 
lUduetUfn Fadon vKtn 4 = 45*. 



A_ 


^ 


7_ 


7;A 


3ogeo8(y-A) 


loj[ fi GOser V 


log«=Snrn. 





o*o 


0*0 


o'o 


O'OO 


O'OO 


0^00 


10 


to-1 


lo-i 


01 


0^00 


ono 


O'OO 


20 


21-3 


21 9 


1-9 


O'OO 


O'OO 


O'OO 


3" 


JS'» 


37 "o 


7'o 


0-00 


0*01 


O'er 


35 


44 '4 


47 3 


14-3 


9'99 


0'02 


O'OI 


40 


57-0 


61-3 


21-3 


9*97 


o-o6 


0*03 


45 


90'0 


90*0 


45 -o 


9-85 


O'lO 


0*05 


50 


90*0 


90 "0 


40*0 


9-S8 


0'30 


ox>S 


60 


90 "O 


90*0 


30 'O 


9 "94 


0'2D 


o't4 


70 


90*0 


90-0 


2O'0 


997 


0'20 


0-17 


So 


90-0 


90*0 


lO'O 


9*99 


O'W 


0'I9 


90 


90*0 


90'o 


0*0 


O'OO 


0'30 


0'20 M 



It will be fteon how rapidly /if and y change near tha 
'C, intrfl<lu>r.ing rapid changua in log cos (y-X) and io 
y. l^ut thcttc aril in oppiKjiC^; directions and practica 
9Dsat« one another, so that the variation in tog » (iho' 
Wt column with a constant omitted) is small. This it 
might expect in the caae midway between c— 90% wk 
decreavca, and < « o*, when it increases aa X inonsaftea. 



\ 



348 Prof. H, H. Turmr, On tht Cl<u$ifica4wn of Lim 5, 

30. We return to the extreme coses, and to the inqdrr 
whether tfat^ available range is utttVicieDt to uotiTbrt oao exiniH 
typu of iiiagiiitudft-curve iiitu the other. The convervioD is mide 
by the equation 

log Bi - log lij - log «| - 1(^ «, + oatiflt. 
= log tan X + const. 
= log tin A - log tAn \ 

where \ i» the latitude coinunou to the two curvea 

31. lleferriug now to Table III., let Hj refer to group VII. hdiI 
Bj t(i group I. ; and let lui in(|uini what values of A. will crmrcr. 
one of these curves into the other. 

Fint mper^jum the niojima. 

The table is arranged on this plan, the assumed maxima fsUirit 
under one another. Subtracting the twelve ordiiiates we get ia 

•00 + '06 + '18 + '29 + '39 + '35 + -14 -"24- "59 - '68 - '58 -aS 

Thesi>, however, are nut difTeruQcvs of logaritlim8 to baBc 10 
Wu mual multiply by about 4 t>j restore the raugt* iu magnituilc^ 
aud by 0*4 the base of the magnitude Rcule, both facton t<4;clbcr 
making i'6. \Vc must aUo Teversi- the Hign?, since int-reitfiK 
magnitudes mean decn^aHinv.' bni:htue».H. Finally we must add Utt 
constant log tun \, ; uud aiuce A,, ia unkuowu, tbrcu sufipuutiau 
are made, viz. A^= 10', A^— 20*, X^^^o', u follows :— 

A«=lo', log Ian A«=9-25 
loBtanx=9'3S 9'15 ^'9^ 878 8-62 8*69 g-oj 9*63 lo-ao ro*34 lo-iS 979 
X^io-o 8-0 $-2 3'*5 2-6 iS 6*1 23*1 580 654 5^-6 ifi-S 

Aj-aO", logtan A«=9-S6 
log tjuj x=9 5* 946 9'37 909 S'93 900 9*J4 9M I0"S« 10*6$ lor49 loW 
A=ao'o i6*o 10*6 70 4-9 5'8 12*6 41-0 73*0 77-6 72-0 4^ 

Afl=3c", log uiii Ao=976 

logUnx-976 9-66 9-47 9'29 9'»3 9"2o 9'54 f 4 071 o'Ss 0-69 «■« 

a.=3D'o 24'* i<?-4 ii'*o r6 9^ '9'' 54'^ 79*"o S^yy ji-^ ^t 

53. The smallotit assumed value of A„ brings the spots at 
ntinimuni too close to the et^ualor, while the largest takca them loo 
close to the pole. In every cu-su the ran>;e required is too huge U 
be probable, though not iniiioMible, Thf^re are, howevfcr, aotue oao- 
siderations which reduce the range. We have eiiperpoMMl Ihi 
obaerved maxima of Table III., but the time of niaximom viS 
certainly I'w altered by u churiKC of aspoct. lu well aa th« tun* ti 
minimum. Further, there is tbe uncertainty about the real titD^ 
of maximum. Both these can be taken account of by troaioe tU 



[Mar. 1907. Long-period VariaUe Stan. 



349 



:ur\'e8 uu [japer and xuperposing them ex|teriinentnl]y, and then 
l>«ading off new poiats on one of tliem to correspond with the 

twelve point) already tabulated lor the other. 

33. Suj}erpfj7iing the eurveg rtnpir trail tj, then, in the neighbour- 
kliowl of [riHxitnQiu, we get new readings for group VII. an follows, 
IgTOUp I. remaining as befurf : — 





Mai. 
























VIL 


■04 


■16 


■28 


•42 


■60 


74 


■90 


-98 


•99 


•83 


•48 


'18 


L 


\x> 


■'3 


•38 


-61 


•87 


1-00 


"W 


70 


40 


'3P 


■'7 


'lO 



l.-Vn. - 1*4 ~ '03 '-■10 + -jg +-XJ +-a6 +•04 - -28 - '59 - "53 - "Si - "OB 

[The range is now from +'27 to -"59 instead of from +'3910 
.-'68 before. Multiplying by x'6 to convert into logaritlimR to 
10 M'e find the values of X when A„= zo' to bo now 

»■* 22-2 140 io'3 76 79 17-6 45-8 730 68-8 49*0 2^*0 

The rt>i|uisite range in latitude h thus ruduced by ^''6 uear the 
pole (frum 77"'6 to 73'''o) and 2''7 near the iquator (from, 4'''9 to 
^"'6), and the improbability therefore sensibly diminished. 

34. A inofih greater diminution can be made if we take into 
account the effect of Mbsnrptioti of the light near the Ktar's limb, in 
addition to the uiniplc furi^slicirtviiiug. In the ubsetiCL' of any iii- 
formatioD ns to it3 amount, it is impo^ible to go beyond a bypn- 
tbetical illuiitmtion. But, as an illuAtratinn merely, if the reduction 
factor for foreshortening and absorption combined were cob- f 
riustead of the previous cos ^ fur f4ireKhort[!iiing alone, thfin we must 
I replace log tau A in the above calculations by 3 log tun A; in 
Other words, we may halve the differenoea 1'6 (L-VII.) before tind- 
iog log tan A from them. 

For the case A^=ao' the values of A woidd now be (for the 
empirical superposition), 

31*3 2i'-o le's 15*1 I2'*6 jrC rSS 3i'7 ^j-o 44-^ ^yo ly-o 

But it is interesting to take another value of Ag, viz. that 
which would be Biipllcable in the case of the Sun. Patting A,j = 
1 1'^, the values of A would he 



112-0 irS 9'4 S'-o 7"-o i'o io-6 i8"'6 3o"-5 2S''o ig's liv 
and wa may coni]kare with these thu values given in the Gruenwif^h 
volumes for 1882 and the following eleven years for the "mean 
distuice from e(|uator of all upots," viz. — 

■ 17-9 13 r I ['3 1 1 -8 10-4 8-4 7-4 11-6 22-0 30-3 18-4 14-5 
Thus a range not much greater than that of Ihv iipots uu Uie 
6uD would, on this hypothesis oa to the reduction fiictior, MifTice for 
converting one of the extreme cases in Table II. or Table III. into 
the other extreme. 



1 



350 Prof. H. H. Turner, On the Classificatiov of utvfl 

35. Thero are a few fitara ontAide these limitrt, as we »Im!i m 
ill § 36, § 37, »o that a ;^eat«r range is roquirt-d. Hut it is tolenUr 
eli-ur that, in defuull uf inforinatlon an to the niagnittide A 
absorption, we cau neither aillrui nor deny tiie $ul1icieTii:y vi thi» 
caufie to explain tho whole range of variation in t>'pu of Uj^l 
curve. 

36. Sa reganU tliis range, one point remain* to be conbiidend. 
How far do the thirty-one stars of Table I. cover the rnTigi- is 
tvpal i\rB there other stai-s much "earlier" or "later" thu 
thewul The bc^st inforraatioii available is thai j;iven in Chandlrr'* 
Third Catalogue and the revised edition, where tlie quantity M -m, 
being tho number uf dayn by which maximum foUowa mininiuiD, 
is Uibithited aloagalde the period. If z {M*m) exceed* tbt 
period, the Btar is an "early" »tar like T Cabsiupcis : if it a 
iw!s than the period, the starts "late" hke the Sun. We way 
takea={2 (M-m)-P}/l' as a charactcrislic of the stAr. No» 
by calculation we tind Lhe minliuuni of group I. in Talile V't. faUi 
at 180° — iS', so that a= -f -lo : anil the ininitnuiu of group VII. 
fnlU at l8o"' + 45'", so that a= - o'25. But these refer to interrab 
lietw^cn cair\ilated maxinm and minima, whii-h differ syeteuiaticall) 
from those as.signed by the observer, »s already point^il out. If 
wti touk ihc obiiervur's maximum we tiliouUl increase a nuniericallii 
iu both cases ; and if vn; assume that the uaiue will be true aUoal 
niinimuu], wn incrvia«d a still further. It would not bo unrcttDo 
able to double the numerical r»nf;e for a, and consider Uiat b 
Chfindler's lists we may expect a range of 

+ -20 to - -50 

corresponding to the range uf + 'lo to - '35 adopted in oom^nu; 
with tlie hypothesis. 

37. In the tirat instance Chandler's Third Catalogue was Ukn. 
and the value of 

a=|2(M-m)-P}/P 

formed for all variables of period greater than 100 day*. Tbi 
results were as follnws : — 







Tablb IX 






a 


No 


of Stars. a 


No. 


of Stan. 


> + •» 




3 - 11 to - -30 




12 


+ *aoto + -io 




5 --31 to- -40 




4 


+ t)^xa 'oo 




12 - "41 Ul- -50 







- "DI to-'io 




38 < - -50 




1 


-•II to- ■» 




38 ToUl 




101 



Tims four cases out of one hundred and three fell uutaide t}« 
limitjj above aaaigned. But on afterwards referring to Cliaodlerf 
"Revision of Elements" (Aetrojujmir.'a! JoiiiTUit, 1904, Jan, &), ii 
wo* found that two caeea out of the four had been altered «o aitA 
fall within the limits, aa the piirticulara given below will ahow. 



lar. 1907. Long-period Variable J^rs. 



351 









TAB1.E 


X. 








Nuns. 


No. 


3nlC»t. 




RcTuion. 








M - /« 


P 


a 


M-m 


P 


a 


S LeoniB 


3994 


125 


190^ 


+ ja 


93 


1S9 


- ^02 


W Scorpii 


5795 


146 


332 


+ •32 


"30 


331 


+ -iS 


V Cc-i^ljei 


8591 


330 


360 


f-'ii 


320 


360 


■f '33 


S Tftun 


IJiiS 


70 


376 


•63 


70 


380 


-•63 



Kurthneir, as regards S Taiiri, it ifi to he remarked that Chandler 

twetity-ooe miixiiaa but only two miuima as the baaU of 

MiiU, iitiU possibly furtlier oWrvatioii may nUor the value of 

- m : and V Ceiihoi only varies 11 magnitude at most, bo that the 

sDchii of maximtitn and minimum are not very »any to determine. 

elicuiiiatioa of two exceptional cases out of four in the 

BeviKioa" of elunienti} 'it uut without t^ixnlBcatiee, and wu may 

>erhaps expect further modihtations in tho future. On the other 

land, one exce|itioiiaJ xUir liaa been intrndiicml in the Itevisiom 

l(X Ophiucbi, see beluw), a star witli small range in magnitude, and 

ilyBCt ta the aame criticisms as V Cephei, 







Table XI. 










TwtlUtf Start wilA Larye Vaitieaa/. 


-. 




+ ■35 


Name. 
X OF>hiuchi 


No. 
66S3 


R.A. 

h ni 

1834 


Dec. GnI. Lat. 
+ 9 12 


+ •22 


V Ceplei 


S591 


2353 


+ 83 


23 


+ •19 


R S L!br» 


55" 


15 iH 


-23 


»5 


+ •18 


W Sco^i-li 


5795 


16 6 


-20 


iS 


+ ■17 


V OpliinL-hi 


5887 


16 Zl 


- 1* 


20 


+ 16 


S Carinie 


3637 


to 6 


-61 


11 


+ *I3 


3 Arietji 


715 


» 59 


+ 13 


43 


+ •12 


T Cassiop. 


107 


18 


+ 55 


5 


+ *ll 


T Caiiricoriii 


7659 


31 17 


-16 


46 


+-■10 


S C«t)Iipi 


7779 


31 36 


+ 78 


23 


-i-oS 


T Cephei 


7609 


21 » 


+6S 


18 


+ ■08 


V Taiiri 


1717 


4 4« 


+ 17 


'3 


+ ■07 


X Cajiricomi 


7577 


il 3 


-22 


44 


+ •07 


W Cypni 


7754 


21 32 


-f4S 


'3 


+ ■07 


U Bootis 


53J» 


1450 


MS 


56 J 


+ •0$ 


V Cygnt 


74*8 


20 3S 


+48 


^u 


+ •05 


R Camelop. 


5190 


1435 


+ 84 


" m 


( -03 


R Aurifpe 


185s 


S 9 


+ 53 


>5 


+ x>3 


WCasnop. 


294 


049 


.58 


5 


+ •01 


R Sa^ptuni 


6905 


19 II 


- 19 


16 

V 1 



352 Prof. H. H. Turner, On the ClassificatwH of LXTtt 



JCTttJ. 



Tablk xri. 

Twtttt!/ Utars with Smaii Vaitu* of 



a 


NAmc. 


No. 


B.A. 

h til 
424 


Dec 


G«l. Ut. 


-•63 


8 Tfturi 


1582 


+ 10 




-•42 


B Aiidrorn. 


112 


18 


-3» 


30 


-'35 


R Gemin. 


353i> 


7 » 


+ 33 


30 


-•34 


S Coroiw 


55«4 


15 17 


*3» 


35 


•34 


R CoiBK 


43' 5 


12 


+ 19 


75 


-•5> 


RCiiiori 


2946 


811 


+ 13 


»5 


•»7 


n U«. Miy. 


38:15 


1038 


+69 


4* 


■27 


V l.yTx 


6871 


»9 5 


+ JO 


5 


■27 


R Cygni 


7045 


'9 34 


fSO 


<5 


-27 


U C!aMic|). 


2*3 


041 


+ 4« 


10 


-26 


R Cenuuri 


5095 


14 9 


-59 


5 


-•25 


• Cetr 


S06 


2 14 


-3 


5' 


23 


H Cnn. Mill. 


2539 


7 3 


+ 10 


IX 


- "32 


Y VL'giiiin 


4492 


12 29 


- 4 


54 


- "22 


8 Hydni- 


3170 


848 


+ 3 


t8 


- -22 


R Aquiln 


6849 


19 3 


-l-S 





- '20 


V OrioQis 


3)00 


550 


+ 30 





- "20 


V BootM 


5194 


1426 


+ 39 


65 


-19 


S Fi«ciitm 


434 


t 12 


+ 8 


SO 


•19 


T Arietiii 


976 


*43 


+ 17 


3" 



In Tables XI. miJ XII. are collecteJ tLe sUrs \rith extmat 
values of a at lioth ends of the series. Further obscrratioDi at 
the ligbt-curvea i>f soiue of these would bs spocially welcumv. 

38. If thi! ptiMuut hyputtieHis, which ciaRsifiiis the stars accord- 
log to the unentiiii'^n uf cLeir uxcs, be curn'ct, it is natural to 
inquire whether auy [jeculiarity of distributiun in spac« » 
MUgi:i'«Uii. In the last culumn arc ^\veu the Galactic Latita<ie&at 
the stars. It trill he noticed that while the stars with, large 
negative vulues of a occur in all Galactic I^ititudea, those widi 
[josittve values do uot occur near the Galactic Pales. In temu eJ 
the bypothests above sketched, thii> would be ihu case if the az«i 
of rotation of these stare were roughly jAratlel to the plane of 
the Milky Way. Wc should tli*-n see stars e<iuuturiaUy in »'l 
directions, but we should not have a polar view of those lying 
near the Galiit-'liu Polcu. 

It TOiiy be remarked that the axis of the Sun is tadined ahonl 
30' to the plane of thw Milky Way. It is not difHcult to soKgut 
pbysicfil reasons for such a gfriievnl con li>;u ration, in view of tiie 
r<4cent discoveries of two steHar systems in relative luotion; hut 
tbe mattrial its so sumll that it would be layiufj; too much atrcas w 
the H>,'Liri's to enter oil such sped ikt ions. At the stiine time th^f 
are sufficiently su^'gesiive to vrammt further inveatigntion. 

39. We have now followed out the consequences of th* 
assumption which first su^^ested itstif, U-uvio^, however, oce 
important point inx lui\.\iet «>\\svifctnX\,o\\ (,% z(i\^ to which we mtm 



g 



Mar. 1 907. Ltmy-period Vai-iahU .Stars. 



353 



return. Bat before doing so it will he convenient to recapitulate 
the main features of the hj'[iothe8in above dealt with, and to jHiint 
out a limitation not hitherto noticed. The chief feature* are aa 
follows : — 

(a) The travelting of the star's activity in lalituiie will mwHfy 
the apparent variation according to the a«pcflt presented to the 
obaerver. 

(b) The travelling i»i lepreeented by a moderate gradient G near 
maxiiiiuiti, and a sharper gradient g near minimuoi, when the 
aotivitj leaves the equator and breaks uut iu high tatitudee. 

(r) Bi>th maximum and rainintTim «rc> diiiplaoed in cunttequenco. 
The amount of di>!placement depends on the gradient and the 
curvature neur the miLxiinum (or miuimom). Near maximum the 
log (activity) in rcpreeonted by a curve, 

and the lof; (forcshortoninf^) by a curve 

and the shift of maximum ia O/aK, Uaing small letters for 
minimum, the nhift is ghk, 

(li) Ntiu' K and k are opposite in sign but nearly eqiml numeri- 
cally. G and 1/ are opposite in Hi^n hut ft i^ greatf^r. Hence 
maximum and minimum will be difiplao^it in the mma direction, 
but the miiiimam mora than the maxinuim. RelativBly to tlio 
maximum the minimum is displaced by 

gl2k ~ 0/3 K = (t}- 0)/2K approximately. 

And the efTective displacement thus depends rough]y on the 
excess of g ovlt G. 

(e) Thift vicvai liependa on the fact that tho spots travel from 
a hi^'li latitude X^ to 11 low latitude \, in a timo (,. and bnck 
over the same di^Umce in a much hhorter time t^ [.et t^=fUJ, 
than roughly we shall have ff = nG, and effective displacement 
-(b-OG/jK 

t* (n - 1) X displacement of mnximnm. 

To get a Urge range in effective diflplarement, therefore, (n-i) 
should be Urge, and therefore t^ small. 

(/) But now coiuos tho limitation not hitherto noticed. Ilie 
period /, is a superior limit for the rlisplacement of minimum ; for 
outside /j the gradient would he no longer g but G, which is 
opposite in sigrt We thus rec^uire t„ to be iarge, which confUcts 
with paragraph (f). 

The val«e of a= {2(M-m)-P)/P accordtux to Chanciler'a 
Cataloi.'Ues ranges* at least from + '22 to - '40 : that is, the minimum 
may fall anywhere between *39P and '70F* after maximum. 

Thus 's<-3»»' 'i>'69P 

.'. n:J>2"2 n- il^-i's 

If we accept the view that the obeervet'a auignment 



354 ^*'"o/- -ff- -ff- Turner, On the ClasnjuuUum. of UtVlI. 5, 

and miniaia ftre systomatically erroneoue, in the manoer indicib^ 
ID ^7-13, the range for a may b« reduced. If we reduce it to <«» 
half [vbich ifl proVtably more than v« are entitled to do), we gat 

It is really straining the pouibilities to give » so largo a valot 
as 4. For one thing, we are allowing nothing; for the change frou 
gradient U V) gradient g \ and for anuiber, we can scarcely admii 
flo great a systematic error in tbe estimates of maximum aad 
minimnin. Probably n cannot exceed %, nnd thus the (.1 ispbicenieL-: 
of [uinimum will he three times th»t at maximnm. and the ffTectin- 
(U^HplnceniRnt aliout twite rhnt at maximum. It followa that t>v 
favimrabk u cuse woii takt-n both in % 31 and in g 33. In th« 
former Mil- lunxima were Miperpueted, wbich makes tbe ciirvee L and 
VII. nt more easily than when both maximum anil minimum ir> 
displaced. In tbe latter, the tit was luljusted Vi l>e even enaier. 

It iH trub that tbtise and other dttliculties in etretching tlit 
hypothesis tu Huit tbv facts con all be rtiuuTed by atisuiiiing a l%ip» 
fliiuUKh ufleut fur nlisocptioti of light ne:ir the limb in additioa v* 
tbe fore><bortf>ning, but there is a natural rnlactonce to draw upoo 
an unknown factor ul' thi>4 kind. 

40. We now return Co § z6, vrhore it was remarked tliat if tic 
facuiu} (lie out altogether at uiinimum, the v■\^\)\-^^ of minimum wiJl 
not W altereil at all. Tbe alteration in ty[)e of curve will thui 
he entirely ilut! to tbe displacement of maximum. This \* • 
complete inversion of our hypothesis: tlie" early" stars wilt now 
he those regarded fr»m tlie i-ijuatur, and the " )at<) " starH thiv- 
ragarded from one of thior pmles. Since the Sun is rt-^rded frr.ri 
the equator and i-* a *' lato " i^tar, there is at first Mgbt un incott.-i.-: 
ency here; but it has Wen already jiointed out how the caer of 
the Sun differs from ths,t of tbe ntar*. owing to the rudimeutan 
nature of the vnriatton. So for as actual calculation goe«, this 
new hypothesis Ate the fads for the Sun better than the old ; fat 
it wan found in § ai that on regarding tbe Sun from one of hu 
poles, his curve became " later " than ever, owing tu the ^esi 
displacement uf maximum. 

41. We fan quickly mu through the work again aud make tbf 
necessary itiodihcatioiis. lietuniini; to Table III., wo now inquim 
what addition.^ to the curve I. will transform it into curve Vlt 
when the miniina are auperpoaed. The foUuwing 8Uper|iositfi>b 
is sufficiently exact to bring out the main features : — 



I. 





[3 38 61 


87 


lOO 


94 


70 


40 


30 


17 IC 


VII. 


32 


48 65 80 


94 


99 


98 


75 


38 


o 


7 JO 



i.-vn. -3a -33 -37 -»9 -7 +' -4 -5 +3+30+10-10 

The difference become-i nearly zero near niinimum, owini: to 
/aculfe dying out aud \Qa.\\n% owl^ Vl^e ^Uatoa^ihafe. Tlie differrnt 



[Mar. 1907. Long-period VanahU Stars. 



355 



from zero tided not concern uh at ])rcseut ; we arc cbieOy concernod 

with the vftriation near maximum, anJ we see that the fiiff«r«ncea 
:are smaller than in § 31, ranging only from +30 to -33, instewl 
fof from +39 to -68. Thua log tan X changes by i'6 x "63= \o 
linstead of by 1 "6 x I'oy = 1 7 ; and A need only chan;,'e fmni 73* 
llo 18° instfuJ of (wiy) fcocu 78' to 5*. But we are met by the 
I'diHicuity that this change from 73° to i8° tniist occur in ahoiit one 

juarter of the p^rioii near m<lj:intum, which is too improbable. If 
[w« now make thp same assumption alwjiit absorption an hcfore, viz. 
{that it converts the toreahortening fdctor cott into cos* 0, or log 

tan X into 3 log tan k, then the range in X becomes 45* to i8*i 
lor 30' to 10" would do. Even this eeoms a large chango in latitude 
[to take plat-e in one-quarter of th« period. It is not imjKwsible, 
. but it acems unlikely. The balance of probabilities aoems to lie 

with the former hypothesis. 

42. Wl- can also Invert thctie hypotheses In another way, by 
'aK.<^un]ing that the maximum i» a time of few fipotA and Die mini- 
mum of many. FSut we !«hnuld tlien find it ditflcull tu get largo 
changes in the e^xicha. At nunimum the photosphere mintt be 
practically covered with spotH, fu that the mcuu latitude could nut 
Tary much ; and at maximum there would be ao few that their 
sitoation could make little difference. 

Thus at present the tir^t hypothesia seems preferable. 

43. One other jioint may be 1>riefiy mentioned. When this 
idea of the variation in li^dit-curve with aspect of the star first 
prea^ntf^d iteelf, it waa tbougbt that it nii^'ht lead tu an explanatiaii 
of Chandler'a periodic terni>i. He givea, for instAnce, the epochs of 
maximum of K Andromeda^ as 

I 2400141 +4io'3 E+30 ain (la'E + go*) 

the mean period being 410*3 daya, but aucce8sive maxima being 
gradually displaced until they fall thirty dayf later than it first, 
and then back uutil they are thirty days earlier, and 90 oti periodi* 
cally. If the axin uf rotatiun of the star were not fixed, but had u 
free periotl of conicAl oscillation, ita aapect to ns would change, and 
eoch variatious in the epoch of maximum would follow. But we 
ahoold apparently have to assume very large usoillationH in some 
well-authenticated caaea ; and there are S'lme, such as S Serpentis, 
for which Chandler gives 

36S-5E + II6 Hin(4"E + 6') 

which the foregoing work aliowe that we could not explain at all. 
' ITie origin of these periodic terms in more likely to lie iu t^ 
cxiatence of several pcrcodicitiea of apot variation with var 

Iamplitudeii, Auch as Frofesaor Schuster has recently diecoven 
the case of the Sun. 



356 OhgervatioM qf Minor Flaia^/rom LXrn. 5, 



On the Jupiter Ewrtion Term. By P. H. Cowell, M.A., F.Riv 

Jn Moutlily Notiee»„ toI. Iziv. p. 417, nad again i» Tol. Izt. 
p. 145, I have shown that tlie ohcervml value nf fchs oocffitaaB 
of the Jupiter Kvactinn term in the Muoii's loagitode «■ 
o'"89+ o""23= + \'-\i. 

In an inten'-atiiig ikajier in the Agtrunomieai Journal^ No. 59:, 
Proreasor Newcomb states that ho has cslculatol the iheoratual 
coefficient of tlii« torui as i"'i5. wberea* Uill and BadAD )uA 
previously agread in giving o''89. 

The mniovaL of the onlj aarioua discordance between ofa»em^ 
and theoretical coefficients for short terms uf a period dan)} 
differing from the puriods of pojt^ible errors of ubeervatiiv 
•trengtlietis thf> co«e stuted in the Mtmthly Notire^, rnl. Ixn 
p. 306, for l/e Verrter a moiu of V«mu against t\xa recent retluctkiD 
by 3 per cent. 



iHoiu of Minor Planets from Photoiiraphu taken with tht 
^o-inch heftertor 0/ the Thompton E<jnat</riai at tht Bopal 
ObserviUory, Greenmch, durt'ng ttie y«ar 1905, 

{ComrnHnkaitd by tin AMronomtr Boyal. ) 

The following positions of minor planeta were obtained freni 
photogmpliH tdkfii with tlie 30-incb Reflector during ihe year 

'905- 

'Ihe plates were ini'Jtfiuroii with the aatrograpiiic micromeler. 

Four reference stars were, as a rule, measured with the plamt, 

their pusitions lieiiig derived when possible from the Catalogues of 

the Astronomieche GeselUchaft. 

The positions piven are nt)t corrected for Parallax. 

log Parallax Correction = log Parallax Factor- log A. 

DaMtndO.M.T. Arparwit H.A. ApiMn-nl Dm. I^ns. Patmllu 

d hnia ttms •.■ 

(407) Ancha«. 
Jan. lo 103043 S 5' 5374 +»7 '4 9 3 -7*556 +0^ 

(78) DUoa. 
Jun. 17 II 4a 14 6 33 31*99 +35 8 ^"^ +9»os +0-410 

(71) NiotM. 
Jill. 17 111546 7« V^ ^'SS ^ V*'"- - 87S5 +©•■ 



)Iar. 1907. PhotogmphA tak&n at Chamwich, 


1905. 


357 M 


t>mUMaiQ.U.T. 

"90S. 


Apfwrenl R.A. Aiipnniil DM. 


Dm. ^^^H 


d 


b lu > 


(270) Analiita. 




■ 


Jm. 17 


11 58 34 


8 43 1576 +15 5 3^'^ 

(374] BlIF^IlIKiU. 


-81978 


+0719 ^^H 


Mu. 9 


10 50 3 


9 s8 l6'04 -0 34 io'9 
(148) QaIMh. 


-» 


+0-839 ^1 


Feb. 25 


12 39 t6 


10 20 12*02 +16 14 45*7 


+ 8*697 


0-704 ^B 


Ukr. 2 


10 lo 5 


10 16 17^4 +17 II 47'3 


- 9037 


+0-698 H 


3 


10 51 44 


10 IS 3060 4-17 23 77 
(93) Undinft. 


- 8-824 


+ 0-692 H 


r«b. 25 


12 4 33 


II 45 1-98 +15 6 367 


-9*113 


+0732 H 


Mv. 2 


10 45 


11 41 46*68 +15 37 31-9 


-9-330 


+0731 H 


3 


II 16 48 


II 41 470 + 1$ 43 48*2 


- 9-306 


+ 0*730 H 


22 


9 46 25 


11 27 30-85 +17 22 30-4 


-9-218 


+0*704 ■ 


30 


9 "9 27 


II 23 974 +17 50 55"* 
(487) Vanetii. 


-9-176 


+0*697 H 


Mir. 30 


10 II 41 


n 52 23*75 +15 5' S7"3 


-9*058 


+0713 ^^H 


_ Apr. 6 


10 22 35 


'« 47 '359 +16 19 36-8 
{350) Omameiits 


-8-635 


+0*703 H 


" Apr. 6 


10 50 45 


11 48 42*65 +37 35 59*9 


-» 


+0-316 H 


8 


10 It 58 


II 47 I99« 37 3» 3 "4 


-8*765 


+ 0-326 H 


T2 


■1 23 iS 


II 44 42-39 37 20 46*8 
(4») I«K 


+ 9-076 


+0*348 ■ 


M>r. 23 


10 13 9 


12 10 56*26 +ti 13 2S'9 


-9*371 


V 


1 ^ 


to 8 34 


12 6 13-43 +13 40 45*4 


-9-198 


-''0739 H 


' 30 


to 33 27 


12 3 24-23 +13 55 i6'S 


-89S3 


+0730 ^^M 


Apr. 5 


10 s6 56 


•i 57 57'4i +14 19 "7 


-8-063 


+ D7|l^^^^P 


1 




<3S) Bclloni. 




^^H^H 


Hu. 32 


10 22 59 


12 3o 39-52 +8 lo'9 


-9*264 


^^H 


»7 


10 33 28 


12 16 53-64 +8 40 53*4 


-9'I74 


^^B 


30 


to 50 32 


12 14 37-46 +9 3 40-2 


-S-93J 


^^H| 


Apr. 6 


9 55 »9 


12 9 41-22 +9 49 57'2 


-9'«A 


m 



3S8 ObservcUiom of Miiwr Plandsfrom, Lxva 

Date and O.M.T. Apparent K.A. Apparent Dec. JLoc- Parallax WtHm- 

i9°5- It~A. Dec 

d hms htne •<» 

(163) Erigoue, 

Hay 5 to 5 42 12 52 32*41 +0 12 I3'i +7'982 +o*Sj4 

8 10 56 51 iz 51 6*68 +0 20 43'5 +9*042 +0'S3S 

(334) Chiuago. 

May 5 10 S3 54 13 58 6-56 - 5 37 36-8 -8-285 +o'**7 

(26) Proserpina. 

May 5 II 21 37 14 31 33-43 -14 29 8-0 -8-448 +0-903 

8 II 44 35 14 28 49-23 -14 21 29-2 +8-518 +0-903 

9 II 7 42 14 27 57-02 -14 19 2'8 -8*296 +0-903 
10 10 44 38 14 27 4-98 -14 16 37-0 -8*693 +0-902 
22 105857 141734-27 -135' 6-5 +S-827 +0-9W 

(386) Singena. 

Jniie23 10 36 6 15 42 6-50 +7 31 19-4 +8*980 +07S5 

26 12 2 16 15 40 4239 +7 22 5-6 +9*373 -fo796 

27 ii 39 4 15 40 17-57 +7 18 46-5 +9-326 +0-794 

(470) Kilia. 

Jime28 10 34 23 16 49 24-46 -9 4! 11-3 +8-210 +0ibj 



I 







(8) Flora. 






June 14 


II 51 44 


I? 5> 37S2 


-19 9 150 


-8-711 


+ 0-917 


14 


12 3 17 


17 51 37-21 


-19 9 "5"8 


-8-506 


+ O'920 


19 


11 37 25 


17 45 59'o9 


- 19 19 14-0 


-8-507 


+0-91$ 


19 


11 so 27 


17 45 58-59 


-19 19 174 


-7 962 


+ 0'9i8 


22 


u 18 9 


17 42 34 77 


- 19 25 30-8 


-S-580 


+ 0"QlS 



(19) Ftirtiina. 

June 23 II 31 16 18 26 4-32 -21 I 20'8 -8-920 +0-920 

26 12 27 II 18 22 55-60 -21 2 1-4 +8-575 +0-92: 

July 7 1045 15 18 n 39-00 -21 4 32-8 -8-648 +0-921 

(47S) Tergeste. 

July 8 10 41 S» ^* ^^ ^*'^S -^ «.S SV^ - 8-810 +o-8Ss 



r 

^ Mar. 1907. Phoiographs taken at Chvenvneh, 


1905. 


359 ■ 


H Dftl«aD<ia.U.T. 
^^ d h in a 


Apfwrent R.A. Ai>pKrent I>m. 


Log. PmllM rteUtr. ^^^M 
Dee. ^^^B 


m 




C46} Heatik. 




^H 


VjuD«3J 


It 4 5-5 


18 50 12-QS - 18 5S 12*3 


-9-214 


+0-908 ^M 


■ juIy 7 


II 7 31 


18 36 36-14 19 12 8'4 


-8-674 


^M 


H 


IJ 6 « 


18 35 37-64 -19 13 19*4 


-8-6oS 


+0-918 ^M 


1 


10 19 33 


iS 20 59-57 -19 36 a6*o 
(313) ClialdiM. 


+ 8-229 


+0*919 ^M 


■July 7 


11 34 45 


19 5 7 9» -5 16 15-9 


-8-667 


^1 


1 


II 59 II 


»8 53 SS'gS -6 58-0 


+ 8-934 


+0-86S ^M 


1 


" " S3 


18 48 54-39 - 6 29 32-3 
(433) Efm. 


+ 8-749 


^M 


B July 19 


13 18 5» 


21 25 5 15 13 49 49'5 


-8-471 


+0-901 ^M 


■ Aog.33 


9 31 50 


ao 24 9-19 - 12 33 OS 

(176} IdUDRB. 


-8-874 


+0895 H 


■ Bcpt 7 


11 26 34 


31 30 467 +12 16 36'9 

{24S] Lamwa. 


+ 9-001 


+0-746 H 


BSept 7 


la 35 


a« 53 73fi - 5 44 68 
C84) CIi«. 


+ 9-062 


+ 0-S66 H 


■ Sept. 8 


12 16 14 


22 37 56-92 -2 27 38-5 


+ 8-882 


*■ o-Sjo B 


B The auuiiyuiouft plauot iliiicavered on iiliotvgniph!) takca on ^M 
1903 Auii. 6, 31 and Sept. 1 ha^ received tlie dcsit-uaiiuii ^| 
1903 LX*, and a pruviiiianal circukr tirbit lias be«n calculated for ^^^H 
it hy Frofeasar Kreulx {Aatron. Nadir., No. 4154). ^^^H 


" Hojflti 


Obtrtator}/, OremmtA: 
1907 .Vareh 7. 

L . 




1 






^^^^^H 





36o 



£ev, r, K Espin, A New Nebula. umij 



A New Nebuia. By the Rav. T. E. Espiii, M-A. 

Oo January iS, while looking for new double atai^ T ata* 
across h bright nebuk, wUich, as far as I am aware, ia au uni 
object. U was estimated to be about 5" ia diameter aud eloa^ 
nnrch. <.}ii Jannary 17 tlie nebula was s^eu for a few mc 
botweuii clouds. (Id February 1 it was well ae«n, a canspic 
object, and equal Cu a 10 magnitude ntax. Tliu elongation 
very marked, and sometimea it looked like tvro DebaUe. 
meaaurea gave — ^ 

Major Axis 6*90 

Minor Axis 6*35 

The major axis was foond to bo roughly at position io*'5. 
aoiall star waa noted S ft. On February 1 1 tbo poutioo 
determined from B. 04-33", 746. Tt was found Ut precede tks 
Blwr by 7""8o, aud ti) be a' 25" south of it. On February iS wi 
(i|)peared to ba a star or nucleus was seen nortb and mt 
U was also mtn on tVbruary 32 and February 23, and ineaMii 
made of it with great dil^culty. The later observattone aeem 
euggext iL ^dautitiii-y nebula, with a .small star at the iiortbero 
The foUowiug are my measuree of the two suirs near Uie nebdn.-^ 



Neb. and star A : — 



19071314 
1424 

Mean 1907*140 



Pi4-9 

'3 3 

13-8 



Neb. and star B: — 

1907 0849 
'314 
»4M 
US' 



Mean I907'i36 



244-6 
244"3 
a45'3 
3384 

243'! 



D 4'io 
4-75 
390 
4-»5 



1675 

<S9o 

'7'o5 
16*69 



Mag. 130 



3 nts. 



Mag. 1 3*0 



4 ate. 




The place of RD + 33'*746 for 1855*0 ia — 
a=3*'47'"»4''8g ^=33° 29' 14' 7 (limn Obn., voL ti.) 

Professor Burnham observed the nebula with tbe 40-izL of tlu 
Yorkos ObsBrvatory on February 20 in moonlight and a «ky not 
dear, and measured the »tar H as foItowK : — 

P 338'-i D i7''86 

and also found for B.D + 33**746 and neb. 

P it3'*9 ^ ^iV'^T wtt^le distancv. 



lar. 1907. 



Obsgrvations 0/ Occuitatioiis. 



361 



ybaercations 0/ OecuJfatiom. By Rev. Leonanl A. Williams, B.A. 

[CammvAicaitd by A. C. D. Crmnmeiin,) 



First Serieg. 

At Stoke Wttke Rectory, 
BlaDilford, Dorset 

I^ngttmte, 2' 20' 5' W. 

Latitude, 50 51 20 X. 

Hei^'hl above !>ea, 440 ft:et. 



At Famiiiubam Vicamge, 
Dartford, Keut 

Longtitude, o* 13' 25' E. 

Liitttuile, 51 23 45 N. 

Heijiht above bcu, 120 feet 



tttarai»l 
Lao II is 4*6 

u71nt COD. 
pXut con. 



Dinppeu-Biioa (l.M.T. 
<l h m « 
i(^S U^y 12 S44 37 
Sept. J9 103540 



HUrMd 
llagtiitude. 



Aug. 29 
30 



2345 19 
2 1345 



DiiftVpcKruirD n.M.T. 
il h m I 

/t Cvti 4-4 1905 Dec. a 53426 

X Le"rii« 47 1906 April 6 7 3 27 
• Saiiictaiii 39 Nov. 19 52930 

<*Cfti 43 1907 Jin. 21 959 

IT nerainoniin4't 26 6 39 55 



MetfiO'i 0/ iletrrmimmj time, — At StokB Wake: I'>ju«l alUiudei! 

vrttli sextant, and artitinial horiion (mercury). At K.-irttiiig- 

bun : M^ridiHti oh^erTatioiia with tnttiHtt instrttment. 
Chronoimler. — Deck watch in box, No. 08354, by Frodeliam. 

lUte jKir rliftn for Jau. 1907, —'9*. 
Jiesuits. — The timca are not ijuaranti>ed tn thw exact fi»c<md ; but 

they are ai^umed, with good reitflon, to he c.(irr«ct to 1*5 

second ■■ 

1907 Jamtary 30. 

Appendix to (he abate Payer. By A. C. D. Crommelin. 

I have reduced Mr Williams' obst-rviittoiis tii the sanio niannar 

'as the Greenwich i)b»mrvatioii8 of occidtutiuns. The R.A., N.P.D., 

and [iiiiDllax of Moon hnvo boeu iiiter[io!iit<>d with seoond dillcreiiceft 

'from the Nautical Altniiuac, and the sumidtameter found by the 

'«qa&tioa log semidiameter =^lug parallux -f 9-43543, thi^ being the 

constaut tv reduce to Stnive's ^emlilianieler 15' 32"'65, which is 

now uted at Greenwich in the reduction ut occultations. Tiic 

]i.A. and N.I'.D. of the stars are takc<n with iLu Nautical Almanac 

values of their mean placets and atur correcLiona. 

Then aMutniup — 
iTnie Timu of Phouomenon=Ob8erved Time + f» 



R.A. of Moon 
N.P.D. ... 
R.A. of Star 

N.p.a. . . 

Parallax of Moon = 



Naut. Altn. value + as" + < x root"- iu »' 
„ 4- y 4- f X mot"- ' 

„ +e 

'/ 



Semidia meter 



Naut Aim. Par*- x *» 72 535 J 



Report of the Melbourne Oi^ervcUory. LXVU. 



I have- found the follon-ing f(|iiatiotis of condiUon ; in the 
of occultationa nbgerveii nt (ireonn-ich, the Gruenwieh r«Iiic 
Semtil. - DistAHcu ts given fur comparuon : — 



Dito. 

1905 May 13 
Sep. 19 
Dec 8 

1906 Ap. 6 
Kov. 19 

1907 Jan. 21 

26 



)-jtl<.-iiliit«<l 
bUtatiee. 



+/ X +» X +|f X +« X +« K -Ml 



-740 =+77 +"62 -77 - ■*< -'43 - -60 -1 

-0-91 =+ii -'99 -'ll +"99 -•19 +t-l7 -' 

-4'lh ^ + 75 - tSi -78 +*6i - '^l ♦ X14 

-636 -7-81 =+-51 +-86 --51 --86 - '37 -297 -1 

-*'33 S'" * + '9a ^'i8 - 92 - -iS - '46 •!- '69 -1 

* I -56 = + ^ + 05 - "99 - 105 - -jfi + I-J4 . 

-3-20 -4*68 = + -87 +'37 --87 --37 --35 - a*i8 - 



[The following were received too Inte for iiisertion in the Anoiai 
Haport of t1ie Goiiticil.] 

Ueport nf tltp MfiJOoume Obeercaiory. {Director Mr P. Hanuthi) 

The principal astro iiomioat work done at this observatorr dariif 
the je&r 1906 wns limited, as in previous yaars and £ur the wu» 
reasmts, to meridian obsurvationii mid stellar photography, incloding 
the lueasurciuciit of plutt'^ of the S^dm'y and Mulbunrne Zodc*. ii 
regard ti> wliich a Kepamti^ r«piyrb i^ appendi^d. 

Merptian (JiMfen*a^i(»«.— These were made with the S-indi 
TnuiHit Circle, and vivrvt aii fullowH : 



Clock Stars 
Azimuth Stars 
List Stan . 



IDIUA. 


ObMrtRUom 
in N.P.O. 


505 


... 


269 


117 


1376 


I3S9 



ToUl 



2050 



1406 



Tlie littt fttaro wtiru selected from tliH Arolbourne platng of \kt 
ABtro;j;rai)hic Cutalupie, to ecTve us fuudamcDtal poiata of ivfereacv 
for Ihs reduction of these plates. 

Thif total number of t.hi.<t olass of stars now completely obaerred 
not less than tliree times jh 5545. 

The reductions, including the preparation of the auDoal rata- 
logue for 1905, are wull advanced. 

A (fODcral catalogue for tliu epoch 1900, including all itar» 
olwerved siiioi> 1894, ia in course of preparation. 

Xo authority has yet been obtained for printing tb« gonenl 
catalogue for the epoch iS^o, the MS. of which was prepand 
some years ago. 




Jlar. 1907. AfcasnrfmciU 0/ Plates, Astroffrapkic CataioffUA. 363 

St^lar Phot<Hfrayhy. — TLo i^teiboume portion of the photo- 
graphic catalogue and cliart of tlio beaveDS lias becu further 
advancad aa follows :— 

WitliUotoiT. BejMMd. 
CLirt IlatM with tripli BxpmaK or sol" «aeh 45 3 

C*t&Ioga« Plates {dupHcata Miiea] .... 19 
Te&t Flftt«9 on, Boiitb Pokr reifioa . . . . I4 
Test Plates on Oxford Type Charts ... 5 

Platea for trials, adjustment of centrs, eto. . 15 

Prolonifed ill-liealth of the obaervera \» partly accountable for 
the Hitiiill pru^rcw shown by tlto above rotuni. 

The astrophotographic work now stanrfs thus :— 

TbA fimt serien of 1 149 plates, covering the entire region, —64" 
to the South Pale, twice, and bhu aeries of chart plates wltli single 
expoearo of onu hour, the centres being at even dejjrues of iloulma- 
tion from —66' to - 90', were conipletfd some time ago. 

A duplicate catalogue seriee is now being made, and of this, 335 
plat«a have been taken and passed na satiafactorj. 

In the chart Herics with triple expuaurea of 30" each, the 
centres being at odd degrees of declination, 519 platen have been 
taken and pasaed as satisfa-'.tory ; 65 plates re«|uiro to be Uken 
again to conclude this part of the work. 

It is inte.n(Ied to extend the aeries of triple exposure chart 
platen to the regionu with centres at even dcgrijca of due [in at ion. 

The following routine duties and other miscellaueous work 
weH carried out for local requirements, as in former yftars : — 

The time eervice ; the weatlier service, compri»ting tha control 
of some 980 couulry Ktationw; the raliuR of clironouwtent fur the 
shipping, and the tcsliug of nautical meteorological and surveying 
tnsLruuienls ; the openilions of the Bureau uf StiindHnl Weights and 
Moa«ure«; the coniinuoua registration of the variations of sea-level, 
atmo.'^pherio elements, seinmic dititurhancen, and the etementa of 
terrehlrial magnetism, iucluding absolute magnetic nieaiureinents 
aud the measurement aud roduclion of hourly ordltiatea on the 
magnetic curves of past years, for the purpose of clearing up, com- 
pleting, and preparing for publication the results of a long series of 
magnetic records, extending back to the year 1868. 



JoiiU RepoH of the Directors of tfu Oimrval'iHen of Sydney 
Malhoume on tfte Metuwement of the Plates of tJiA Ast< 
graphic Catalogue. 

The uiBasurement of catalogue platea obtained ' 
observatories was continued by the Bureau eatublished 
purpose at the Melbourne Obsenrat^iry in iSgK, and (rfi 
tained at the joint expense of the States of New South V 
Victoria. 



364 Measurement of Flates, A^rograpkic CettcUogtu, LXTIL5. 

The work of the year 1906 was carried out by the nsuI 
temporary staff of six young ladiea, assisted by a permaoent offini 
of the Melbourae staff, usiog the same measuring instraments, utd 
following in every respect the same methods as described in reporti 
of former years. 

^he numbers of rectilinear co-ordinates measured during the 
year in the direct and reverse positions of the plates are as follows :— 

149 Sydney Plates, containing 75,162 stars. 
181 Melbourne Plates, containing 45,069 stars. 

The total aggregate numbers of plates, etc measured to jist 
December 1906 are aa follows : — 

562 Sydney Platen, containing 325,978 stars. 
836 Melbourne Plates, containing 268,714 stare. 



ERRATUM IN ANNUAL REPOKT. 

Oq p. 29S insert the nkme of Prof. E. E. Barnard in list of Donon to tbt 
Library. 



MONTHLY NOTICES 



OP THS 



ROYAL ASTRONOMICAL SOCIETY. 



Vol. LXVII. April 12, 1907. No. 6 



H. F. Nbwall, Esq., M.A., F.R.S., Prbsidbnt, in the Chair. 

Arthur Neville Brown, M.A., Ludgrove, New Barnet, Herts ; 
Harry Cooper. 19 Cromer Road, Eastville, Bristol ; 
Phanindralal Gangoolj, M.A., University. Calcutta, India; and 
William Neirsam McClean, 42 Durdhum Park, Bristol, 

were balloted for and duly elected Fellows of the Society. 

The following candidates were proposed for election as Fellows 
of the Society, the names of the proposers from personal knowledge 
1)eing appended : — 

Mtyor-General Henry Herbert Lee (late R.E.), The Mount, 

Dinas Powis, near Cardiff, South Wales (proposed by 

T. E. Heath) ; 
Augustus Kdward Hough Love, D.Sc, F.B.S., Sedleiau 

Professor of Natural Philosophy, Oxfonl (proposed by 

H. H. Turner) ; 
Rev. Reginald Wm, Bickerton Moore, M.A. Oxon., Vicar of 

St James', Bath, 1 1 Devonshire Buildings, Bath (proposed 

by Rev. D. Higbam Sparlin<;) ; and 
Herbert Gerard Tompkins. Examiner of Local Fund Accounts, 

N.W.P. and Oudfa, Lahore, India (propost-d by S. A, 

Saunder). 

Anders Dooner, Director of the Obs(.'rv,itory, UclHinjifom, 
Russia, waa proposed by the Council as an Aasocuv^^.^ i^l \,\\% 
Society. 

2*> 



366 Sir David GUI and Mr S. S. JTuuffh. UtTOI 

Kiglity-eiglit presents \rQre annoni)c«d ax liaviog been reoeittA 
aiucB the l.u^t tneetini;, including, amonp8l allien :— 

Besmi^^n ObaenrAtory, Bulletiu A)ttronomi<]^ue, BuUetiu Giiv€»- 
uuStrique, Bulletin Mcttkirologique, etc, pn-sented fay the 0\att 
valory. 

Aetrojtnipllic Chart of the beaveiis : 20 ch arts presented hj iht 
Koyal OViservatory, (Jn-eiiwich ; 47 eburte from the Pari«, AJgien, 
ami 'I'milouxe Ol-nervatorirs, prenented by the Froncli MinUdcr fli 
Public lustructton. 



VetermiwUiow of Penouat Ktpiation depending nn Ala^AJi. 
luaile with the Trangit Cirrh-n ami thu Heliometer at the Bof^ 
Ohifrmtoty, Caps of GoOil Hop".. By Sir l^avid Gill, K.(XB« 
F.K.S., and S. S. Hougb, F.R.S^ H.M. Aatrouomer Kt lb 
Cape. 

Tho obsorvatioim here discnssmi were planned at the time 
a tlisciisfiion bad arisen Wtwefn Mr Hinks and Or Cobu ' u 
tliu cxisteuL-e of pcrwnaliiy de|H.'iidiii^' on uiuK'iitude io tniuif'' 
obat^rvatimis tiinde by the Uepsutd truvolHng wire method. 

'Dk^ question at iftKite is so iitiportatit in connection with 
future of meridian o)»erTation, that it appeared desirable to di 
a considerable amount of time and labour to its aettleiuaut. 
position of a bri;:lit star rt-luiivo to two syminetri caller n'tiiit 
faint stars of equal nia^nitude can be determined bv meaat 
heliometer obaervations irith graat preciaion and absolute fr 
from personality. With the modern heliometer the iniagee of 
brighter ntar can be reduced by^ tneanit of screens to ni 
with the images uf the fainter stars. Even if we grant that 
may be a pei-sotiality depending on a residual apparent dif 
of ma^rnititde betm-ecn the image uf the star whose hri^bcncH 
reduced uud tlxat of the other star under nieLasuruuient, it i* ii 
possible to imagine that the obaerrer can be atfecivd by 
difference of pertiotiality iti the measurement of distance of 
pairs of stars whero one component of one pair pr«c«de« aad 
other follows the star whose magnitude has been rodacMl by I 
acr«en, becautc the two conditions of measnrenient an: 
similar. 

Farther, if the measures uf both distances art* mode simolt 
oualy (t.i>. in the order a, h, h, a), the instantaneous scale- 
must be the aame for both. Then, if we siipposu the poatiaft~ 
angles also to be measured, we can intrxluce both the scale-Tslv 
and the index error of the pusition-circle as unknown quaniitM 
and determine the R.A. and Dec, of the brighter star relet) k ^ 
the fainter stars — free from all personality. And if the diffenacp 
of decliuation are either very tnnall or accurately determined, «* 

• JIfcrttlUy Notice*, \x^v- *3i\.MA A*. Hodv-.^-s^^ ^^^q^ 



Lpr. 1907. PerJtoiuU Equation depending on MagnUtbde. 367 

letenuine 'Hrectly ttie U.A. or the brtglit star relative U> the mean 
\A. of the faint starK, free from perwiital and oilier systematic 
rror. 

We Imve in our experioQce at thu Cape many iastances of this 

llreediitii from porsooality in heliuraeter observatimis, of wbicb a 

[Tery good instance will be found in tbo AnniU$ of Uie Cajte 

VMerratory, vol. viii. part 3, pp 73B-81B, in comiectioii witli 

le determination of th>d pitnillftx of fi Crucifl hy r>ill ami Finlay. 

lere we have ohservatiotis of the distances of two stare of 6J and 

[7 Timgnitndi- in alitiosc exactly opposite directions fi'uni ^ Crucis, 

ml situntRd ac distaiions of 3812' and 5434' roxpectively from it. 

l,Cigll measured thfae diMtanrefl on ievtintet>n nighta, and Finlay on 

ifte'r'n night:*. In foraiinj; the equations of condition for deter- 

[inining tho parallax, the liifference of the two distances fur 1S90 

liira* a»fliin)ed to bo 622""05o+a;^ for Gill, and 622'*o5o + ic, for 

<i[ilay. The simultaneous eolation of the equations gare 

j*g= -o"'ooi ±o''oi9 
ar,=* -0 'oji ± "023 

id the probsble ermr of the ainf-Ie obaervation ±o''077. 
But if vru regarded Xg='X/, the probahle erri'r of the single 
jbservation became +o"'o74. 

The Latter hotutiou is tbiia the liettor of thu two, proving that 
lere is no sent^ible »y8tematic dillerence in Ihe determination ot 
the position of fi Crucis by the two obserrers. 

About the time that the afii^r-nientioned operations were 
ommt^iiced. the completion of tlie current Catalogue with tht: old 
Pransit Ciirlu left tliu ob^crVHrii frue to make simultaiieouti 
sbservatiaud with tlie luiter, and a veritication of their personal 
lualioii depending on nmgiiitudc, derived some two ytjare 
jrevioualy by the screen method, was tlnis rendored as convenient 

it wad desirable. 

The groups of stars 8ei<?ct«d consisted of three stars approxi- 
ktetj on the arc of a great circle and, as nearly as coidd be 
tosen, equi-spaced. The middle star was on the average of about 
j^ iinif^nitade, and theprece<iiiigiind following atara on the average 
ibout 3^ magnitude. Tlie difference of R.A. was always large 
iiougli to allow of all thn-e Ktiirs l>eing oUsorved without undue 
laste on tbe same night, while the (]i?tan4:es were re-stricted by the 
limitation that they must fall within the r.inge which couU be 
Ji«a*»red by the heliometer, viz. about a'. 

The transit observations involved ihn tnuisit of each of the 
irce stars io succession, so thut their differences of U.A. could 

derived independently of cloe^ arror or other iustrumontal 
]jU8tnientB. 

The heliometer uieasureiuents consisted in the measutomeut 
>f distance and position- angle of the bright htar from each of tX 
liuter ones of the group. Krom these otutervations the ^oiaXm 
)f the bright star relatively to ihi;; two fainter ones c&i\ \)b dATV<t 



368 



Sir David GUI ami Mr S. S, Hmigh, 



Lxntfl 



independently of the instantaiieoua xcale-vahie or imlex oomocM 
to the poHitioii-circl« or otbei' «<|tiiiloriaI adjuafcmenu u( ^ 
h',-lionjft«r. 

The i«t1o[itt!cl rtiftgnitiides of the xtara Hhto been tnlten wW 
possible from tliP Harvanl Photometry. For Btani not couUinW 
therein, the muKiiitutltis are derived ireni ustiniates made br *if 
Transit Circle obnttrverg, using, us standards, atara whose msi^tiitiidd 
have beeu delertuined at Hiirvanl. 

The folIowJTi^ i» ii list of t1ie groups obKerved, nambend oo 
Recntirely in order nf U A. The initialn n, b are used to diati&xtoib 
the preceding aivd following pairs of the group. It ebualid be 
noticed that in souie cases the sanio hriKht star has Ihwu u»a) it 
iiioro than one groxip. For siMiplicity of rfduction, hoirevtr, uu> 
groups have been treated as if they vere indepeudent. 



Table 1. 
Lilt of Afagnilude Ptnottal JSpuMon Stars. 



^M 


5«ma. 
B.I>. Ho. 

'3'. 3882 


87 


B.A. Dk. 

fa m ■ 
16 4 41-01 - 3 17 g6'i7 


H 


a 'Jpliiuchi 


31 


16 9 25*10 


- 3 »7 91* 


■ ' 


- 3". 391$ 


8-3 


16 12 4875 


- 3 ♦* M 4* 


■ " 


-*S'.S787 


87 


16 18 3-23 


-»6 3 45* 


■ 


a Suorjiii 


'•3 


16 23 38-51 


-36 13 Jii* 


w ' 


- 26-. 5678 


S-5 


16 29 28*55 


- 36 t6 st-l» 


1 ' 


10', 438 J 


8-3 


16 40 io'37 


~ )0 29 36 91 


1 


2o0p1iiuL-bi 


47 


l« 44 37-97 


-10 37 tr, 


1 


- Id", 4403 


8-3 


16 48 22*13 


- lo 35 5«^ 


1 


-15°. 4439 


87 


16 58 40'38 


-16 3 37^ 




7 Ophiucilii 


2-6 


17 4 5914 


-IS 36 3111 


b 


- 15'. 45«2 


67 


17 ID 53*66 


->S 7 ft* 


5- 


+ 1*". 3»34 


67 


17 35 59^98 


+ " 59 4ST< 




a Opiliucbi 


2'I 


'7 30 34"24 


■*-i^ i7 tPli 


b 


-* 13% 342' 


6-3 


'7 34 i^13 


+ JJ a 5171 


6a 


- 9°, 4616 


8^ 


17 46 4971 


- 9 57 «3*i 




r Opliiaolii 


3 5 


>7 53 51*07 


- 9 45 WW 


h 


-9'. 4646 


8-6 


tS D-97 


- 9 35 «3 


7 « 


- 3'. 4*55 


95 


18 8 38 -S3 


- 3 04*^ 




7 Servontia 


S*5 


tS 16 267a 


- a 55 itll 


b 


-3%^&# 


*^ 


\'i> -v^ 1ft- %f^ 


- 3 50 o« 



Apr. 1907. Personal Bquation depcndinff on Magnitude. 369 

Tablr I. — eontinunl. 

Oronp Name. Mag. RJt.. Dm. 

No. B.D. No. 1906*0. 

_ . h m ■ • « « 

» « -4 , 4557 9'2 18 37 23'90 - 4 54 o"99 

6 Scuti 4'5 18 42 11*22 - 4 50 56*03 

6 -4°, 4603 9*2 18 47 50-28 - 4 50 38-87 

9 " -5°. 4835 9*1 18 55 25-09 - 5 30 7-85 

A Aqiiilie 3-5 19 1 15-63 - 5 I 25'8l 

h -4', 4719 8-6 19 7 2399 - 4 37 "'97 

10 « -5". 4845 8-3 18 57 50'si - 5 40 1773 

A AqnilK 3-5 19 I I5'53 -51 25'8l 

b -4°, 4712 87 19 5 I5V9 - 4 12 iO"S7 

11 a +2°, 3856 7-8 19 15 5570 + 2 45 43*" 

8 Aquilffl 3-4 19 20 45-54 + 2 55 36*95 

* +3°, 4043 6'4 19 25 50'94 + 3 M 5172 

12 a +3% 3990 8-8 191742-36 +3 9 33 "36 

8 Aquila 3*4 19 20 45-54 + 2 55 36*96 

b +2°, 3892 5-9 19 23 37 '64 +24418-32 

13 a +8', 4198 8-4 19 39 50-81 + 8 51 55*66 

aAquilse _ O'S 19 46 1 1 "83 +8 37 10-64 

b +8°, 4275 8-0 19 52 2175 +-8 II 48-34 

14 a +8', 4227 9*0 19 44 39-25 + 8 22 10*96 

a Aquilte o'S 19 46 11 '83 +8 37 10*64 

b +8°, 4247 S'2 19 47 57-91 + 8 53 20'02 

JS a -q", 3911 8-6 20 2 i-oi - o 24 11*00 

B Aquilffi 3*4 20 6 27'3i - I 6 2-36 

* -1°. 3935 7'5 20 II 34-11 - I 47 16-90 

S6 a -I*, 3902 8-0 20 4 31-69 - t 32 57-82 

6 Aquiire 3'4 20 6 27-31 - 1 6 2-36 

6 -0°. 3942 7'5 20 8 i4"67 o j6 47'98 

17 a -18', 5663 8-5 20 18 1075 18 31 102 

IT Oapricorni ■ 5T 20 21 5651 iS jr la^.s 

6 - 18', 5705 8-3 20 26 267 iS 2,1 0-52 

18 a -5°, 5349 79 20 37 31-64 s 3« 'J'S 

3 Aqusrii 4-5 20 42 46 70 5 22 zuio 

b -5', 5402 8-5 20 47 21 7H ^ 7, ii 11, 



370 <Siir David GUI avd Mr S. S. Hough, LXTn.4 







Table I. — eotitiimed. 




Groan 


Nmme. 


Hag. 


B.A. 


Dk. 


No. 


B.D. No. 




h IB ■ 


go6-o. 


19 a 


-5". 5368 


77 


20 38 58'33 


- S 55 44« 




3 Aquarii 


4'5 


20 42 4670 


- 5 22 20-10 


k 


- 5°. 5395 


81 


20 45 45103 


- 5 83084 


20 a 


- I?', 6140 


8-3 


20 55 1077 


- »7 U Vi-^l 




9 Capricnrni 


4'i 


21 39*87 


- 17 36 24*39 


ft 


-i8", 5886 


8-3 


21 8 31*41 


- 17 57 9 39 


21 a 


- 17". 6167 


7-6 


20 59 34-81 


- 17 32 13*51 




9 Caprifomi 


41 


21 3987 


- 17 36 2439 


b 


- 18°, 5862 


60 


21 2 27-97 


- 17 49 58*95 


22 a 


-6', 5757 


8-3 


21 21 37 93 


- 6 24 29-01 




3 Aquarii 


3*0 


21 26 36-68 


- 5 59 6T 


ft 


- 5". 5592 


77 


21 31 3679 


- 5 38 2265 


23 a 


- 6°, 5761 


8-9 


21 23 5*00 


- 6 I 4373 




$ Ar)iiai'ii 


3'o 


21 26 36-68 


- 5 59 6" 


ft 


-6', 5782 


8*8 


21 28 57-14 


- 5 53 47'5» 


24 a 


+ 9°, 4871 


8-9 


21 35 ^1'07 


+ 9 33 42^93 




( Pegaai 


27 


21 39 34-15 


+ 9 26 37-45 


A 


+ 9°. 4**99 


87 


21 43 23-01 


+ 9 24 36'9i 


25 a 


+ 5'. 4947 


77 


22 58-56 


+ 5 30 32t>9 




B Pegasi 


37 


22 5 27 -48 


+ S 44 6-^5 


ft 


+ 5°. 49^2 


8-5 


22 10 51 -38 


+ 6 ID 2960 


26 a 


-11", 5S23 


80 


22 19 31-52 


- 1 1 37 58-19 




a A([uarii 


4-S 


22 25 40-44 


- 1 1 9 32 79 


b 


-11°, S!57S 


8-9 


22 31 41-51 


- 10 46 31 '29 


27 a 


- 14°, 6337 


8-6 


22 39 59-06 


- M 7 52'55 




T Aqiiaiii 


4 "4 


22 44 36-92 


- 14 5 21-01 


» 


- 14", 6367 


8-9 


22 50 25-35 


- 14 14 2S-93 


28 a 


+ 15°. 4737 


90 


22 54 12-54 


+ 15 16 4373 




a PcRasi 


2-6 


23 4-66 


+ >4 41 5777 


ft 


+ '3°. 5059 


7-8 


23 5 16-14 


+ 13 55 7!i9 


29 IE 


- 20°, 6568 


87 


23 ti 40*04 


- 20 28 29-33 




b' Aquiirii 


4 3 


23 18 2-08 


- ao 36 4997 


ft 


- 20° , 6606 


%■% 


^'i'^S <J7o 


-20 41 22T39 



Lpr. 1907. Persitnal £qwUion depending on Magnitude. 371 



Tablr I. — (Oniinutii. 



Group 
Ko. 


B.D. No. 
-15*, 6462 


MKC. 
8s 


R.A. 

Ifof. 
b Bl s 

23 32 3246 


'a, 

- 14 44 li'*J7 




«' Aqunrii 


4*5 


23 37 508S 


-»5 3 53'03 


I ' 


-1 5", 6500 


8-9 


23 43 44»4 


- 15 22 50-19 


U 


+ 5". 5230 


8-4 


33 48 1979 


+ 6 10 34-47 




w FtKturn 


4-0 


n S* 29^3 


+ 6 20 34-66 


fr 


+ 6*. 524a 


78 


3 15*15 


+ 6 2] to'58 


3aa 


-9'. "3 


8-5 


7 33*83 


- 9 13 S6'9 




iCett 


37 


14 3833 


- 9 30 4r89 


1 ^ 


-9", 79 


8-0 


22 33-65 


- 9 10 40"a5 


33 « 


- is*. 98* 


8-8 


31 3379 


-18 7 4r30 




eCeti 


23 


38 52-31 


- 18 3a 8-60 


b 


- '9'. 133 


86 


45 59-89 


- 19 1 2 23 



The remiltn of the observations are contiuned ia the f<Jluwiag 
Tables II. aud III. 

The transit. nWrvations have been made by aaveii diffarmit 
Kburvens twn lifting ihe oM Transit Circle and reconUrig the times 

traoHt over fixed wires in tlie usual Tnaniitr by meauH <if a 
lograph, anil the n-maininff five oMervin^ nitl] the now 
rovei-ftible Transit Circle by mean.** of « tnivt^lhng wire guided by 
han'i, and antomatiMlly recording on the cbronograph the instanta 
when thi; wire reached certain lixed piwilioiis. Tha resulta havH 
been n^ferred to LhH et^iiinox 19060 by the applii-ation of the 
uaual star-ooiTCctionu. Table II. cuntaina Ihe observed differences 
of R.A. Jt-rived by the di(fen>nt observers after uiiplicatiuii of 
these cnrrectioiitc, the Rutfixea indicating the mimber of Mparate 
o1>serTalionB involred in each result. 

The holiometer measures have been made by two ab^errera, 
Measre Whittiiij^'dale and Bahlwin. Tho results ([iioted in Table 
III. ax» the mean rei^inlts from ail the meamires of each pftir. 
They hare been corrected for refraction, but, except in a few casM, 
DO corrections for aberration or imtati'<u hare been apuliod. 
thew qnAiititics will bo pr.i<;ticully eliminated simnltaneni' 
the instrtimental ^cale-constant and index correction t 
crrclfl 




^m 373 


Sir David QUI and Mr X S. Hough, ^H 


^k 




Tadls II. 




■ 


^^^H 


<^t«ervtd Diferfnuta of Right Aaeauttms. 


■ 




' 


R|)ocb 19060. 




^ 


IsttnunoDL 8-Inch Tnuiitt. 




B«Tcnll>l« Tnuiitt drol*. | 


Obtmrvmr. Power. 


Pc«d, ^ 


Wiililr. 


JefFnea. 


ilUlUa. 


WomL fl 


m • 


m ■ 


IB « 


m • 


in • 


■ 


t a 


4 44'o75s 


4 44'3Si 




... 


- 1 


i 


3 23*69ai 


3 »3'597i 




... 


"M 


2 a 


S 3618S1. 


5 36 130« 




5 36-aa5, 


...V 


h 


5 So-otSt 


5 49'970a 




5 49 93Si 




3 a 


4 »7*5J4i 


4 27-564, 




... 


4 »7*5a«i 


fr 


3 44*17*1 


3 44*Hli 


... 




3 44*1511 


406 18*6941 


6 18-64;, 


6 tS*679i 




6 18709, 




> 5 W470| 


5 54'557, 


5 54 '51*1 


... 


5 54*47»a 




5 a 4 34146, 


4 34" "68* 


4 J4ioi« 


... 


4 34 '2791 


4 34'3S9i 


A 4 4'S'a, 


4 4-5084 


4 4-4S5a 




4 44551 


4 4 -455. 


607 i'ai7i 


7 "'IS?! 


7 I 'arttj 


7 l*«7i 


7 1 •242| 


7 I*3i0i 


b 6 9-909, 


6 9 •945* 


6 9-873« 


6 9-8991 


6 9-917, 


6 9-84», 


7 a 


7 47742» 


7 47'SHt 


7 47 763, 


7 47«*»i 


... 


b 


7 53716, 


7 53*6y>a 


7 53722, 


7 53 "6701 


... 


8 « 4 47'277i 


4 47 'IS** 


4 47'28ii 




4 47*263, 




ft 5 39'oS4i 


5 39'oS84 


5 39''>4S, 


... 


S 39"o»Oi 


"u 


905 50 477j 


5 5o*447« 


5 5O'50"* 


5 50526, 


5 50-5641 




» 6 8-389, 


6 8-416, 


6 8-3564 


6 8-351, 


6 8-313, 


... 


10 a 3 ZS»44* 


3 25122, 




... 




... 


ft 4 O'tlSf 


4 o"<673 


... 






.. 


II a 4 4978^4 


4 49 7 3^ 


4 49'Si9i 


4 49*833, 


4 49'79S» 


4 49'S46| 


A 5 5 "32*4 


5 5 4037 


5 5356, 


S 5'333> 


5 5*365, 


5 5-356. 


12 3 3*194, 


3 3' '62a 


... 


... 




... 


ft a $2*048, 


2 52*099^ 






... 


... 


13 a 6 20-946^ 


6 30'9I3. 


6 30*956, 


6 30-946, 


6 31*017, 


6 21 'Dl^. 


ft 6 9S67i 


6 9-870^ 


6 9-S76, 


6 9-785, 


6 9776, 


6 9tiojc 


14 a I 32*5484 


' 3a 537. 






... 


■ K 


b I 46*043^ 


1 46*083, 




... 


... 


... 


15 a 4 25-M34 


4 263514 


4 36-384, 


4 26-25I, 


4 26 336, 


4 36-3T91 


ft 5 6-7684 


5 67594 


5 6761. 


S 677s, 


5 6743* 


5 67581 


j6 fl r 5S"63*» 


I 5S'639* 








... 


» I 47-3324 


1 47'3Sii 








jd 



1 


Apr. 1907. PersomU Equation depending on MaptUufU. 


373 1 


H 






TabL* II.— »ii«ni«irf. 




J 


w 


iiBtnk S-hich TruHtt 




tUranible TntMlt. Clrote. 


«■ 


rttr, Prtwer. 


PMd 


Wilkin. 


JaBrlo*. 


MuUU. 


Wood. 


JKclann. 


^^K 


■1 ■ 


m t 


IB • 


m 1 


■n ■ 


Ill ■ 


■u ■ 


^K 


J *5'8*'. 


3 457871 


3 45-816, 


3 45-761, 


3 45 Si a. 


3 4S777i 


3 45 78i» 


B 


4 6-0914 


4 6104, 


4 6-0S6, 


4 6-141, 


4 610a, 


4 6-148, 


4 6-141. 


B 


5 15 0191 


5 »5"oaJt 




5 '5023* 


5 <S*<M7. 


5 «5*os8j 


S >S°4B 


B^ 


4 3S'»J. 


4 35*>aa« 


... 


4 35"097« 


4 3S*oS9i 


4 35076, 


4 35^0319 


B 


3 ■>8-36i. 


3 48-3571 




... 


... 




... fl 


B 


2 58-309, 


2 58338. 


... 


... 


... 




... B 


B 


6 49i*5i 


6 a9-i»9, 


6 29-078, 


6 29*183, 


6 39-Mt, 


6 29-1 16» 


6 29*1491^1 


B 


7 Si'533i 


7 5' 5241 


7 5''5«, 


7 S<*5o6i 


7 5'*5'o» 


7 S»'5»7. 


7 5i-48a9 


^m 


1 S'oj'i 


r 5023, 




... 


... 


... 


... B 


B 


1 48093* 


I 48'oS7, 




0. 




... 


... B 


B 


4 587a7» 


4 587551 


4 58725, 


4 58752. 


4 587451 


458746. 


4 58757. 


B 


5 0103. 


5 oo77i 


5 0-1 a?, 


5 o'ia44 


5 o^Ji 


5 0-124. 


5 0-itq^ 


B 


3 5i66r, 


3 3' '5781 


... 






... 


' I 


B 


3 20-476, 


2 »-47a, 


... 


... 




... 


1 


^m 


4 7 •040* 


4 6-987, 


4 7 ■017, 


4 7"<»4* 


4 7-077. 


4 7-o86| 


4 7-044M 


B 


3 48S9'* 


3 48-918, 


3 48-858, 


3 48-872, 


3 48-843. 


3 48 844, 


3 48*865,^ 


B 


4 a8"907i 


4 28-878, 


4 18-858, 


4 28-907, 


4 28-870, 


4 2>i■iiS6^ 


4 28-9074 


B 


5 a3-8«5j 


5 33-9731 


5 a3-9i3« 


5 23-897. 


5 2J'9a5» 


5 23 '9 184 


5 23-894^ 


B 


6 ii-S72i 




6 8-880| 


6 8*901, 


6 8-903, 


6 6*918, 


6 8-923, 


B 


6 1094, 


... 


6 1-012, 


6 1079, 


6 1*040, 


6 1037, 


6 1 -078, 


B 


4 37 •8441 


4 377961 


4 37'875i 


4 37-8461 


4 57-824, 


4 37*875. 


4 37-8491 


B 


s 45-458, 


5 48-53'. 


5 48-443i 


5 4S-437, 


5 48-468. 


5 48-4344 


5 48-3901 


B 


5 5a*»4o, 




5 Si*'09. 


5 5«i64i 


5 52-071. 


5 52-123. 


_ 


B 


5 "•474« 


... 


5 "•473» 


5 11*478, 


5 11-506, 


5 n-453. 


... 1 


%« 


6 »2*o7o, 


6 21-909, 


6 22-031, 


6 21 ■9«4i 


6 23049* 


6 22-021, 


6 3a-oo4gS 


b 


7 7'63'i 


7 7-670, 


7 7-618, 


7 7*6301 


7 7603, 


7 7-5891 


7 7-637. 


a a 


5 '8 53^1 


5 '8-395i 


5 '8-458. 


S <S 393i 


5 '8 426, 


5 18-480, 


5 'S-i95i 


b 


5 S3'25i 


5 S3'394i 


S S3-3i3t 


5 53'375i 


S 53 '339. 


5 53 309. 


5 53 MS. 


« A 


6 9aS7j 


6 9'to6j 


6 9-336. 


6 9266, 


6 9-234, 


6 9-2581 


6 9'24i, 


' b 


7 462 1 5i 


7 46213, 


7 46 0991 


7 46-099, 


7 46191. 


7 46-0941 


7 46-1 1^_ 


« « 


7 4-3851 




7 4-3*8, 




7 4*506. 


7 4-490. 


' ■ 


b 


7 S544'i 




7 55*a8o» 


... 


7 55*95. 


7 55*310* 


' ■ 


S " 


... 




7 '8-515, 


7 IS-S76. 


7 i8*537i 


7 i8'559, 


' ■ 


'■ ft 

to. 






7 7-585. 


7 7-586, 


7 7-642, 


7 7-573, 


4 



374 


Sir David aUt and M>- S. S. Huu^h, 


Lira 6. 






Table HI. 




^j 


Oronp. 


TahU of 
So.ot 

UOB. 

D. P.A. 


with Uu BelivmtUr. 

a. 


i. 


D1*Ubc«. rMlUon-Aucle. 


t>M«uc«. 


PcMlUn»-4KbL 


1 


3 » 


4289 419 277 59 48 


3399-816 


^3 ^^^ 


2 


3 ' 


4569-911 27S 23 13 


47" 909 


»73 9 Jl" 


3 


3 1 


3971132 277 9 IS 


330(^70 


a69 26 3» 


4 


3 2 


5702-217 154 19 


54*1-158 


asi 34 5' 


5 


2 2 


4617-319 241 3 32 


44837 IT 


333 33 )3^ 


6 


3 » 


6363*879 364 14 34 


5506*352 


263 49 SM 


7 


3 ' 


7015-268 267 58 24 


7103-951 


*67 57 ^^ 


8 


3 ' 


4397*166 368 7 13 


5067526 


27< 44 'fl 


9 


3 a 


5510-700 252 23 22 


5693-633 


ass 46 5'" 


10 


3 3 


3^49927 233 iS 15 


4650*005 


331 6 14 


II 


4 2 


4381*633 «6a 47 I 


4716^7 


356 sj 16 


^^^H 


3 * 


2868*977 287 32 12 


2665 VI 2 


285 is*i 


^^B 


3 2 


5716171 279 28 13 


5693-49' 


286 4 t& 


^^H 


3 3 


1643*636 237 31 33 


1845856 


238 55 a 


^^H 


3 3 


47'7*547 30a 44 44 


5332-509 


I9» S' >* 


^^H 


3 3 


2369-918 227 36 35 


3380 '70s 


233 6 4> 


^^H 


3 ' 


3211-763 270 46 3* 


3338-059 


363 31 31 


^^H 


3 2 


4796-276 259 16 9 


4263-023 


^55 4 4» 


^^H 


3 3 


3954-919 240 6 58 


2789*353 


aS3 M 37 


^^^H 


3 2 


S7i9-49> 283 45 15 


6848-518 


38t 2 45 


^^^^H 


i 3 


963 S25 285 4* '7 


'745 "713 


39S 33 20 


^^^H 


3 a 


470853* aS' 41 S5 


4843-676 


24S 12 41 


^^1 


3 ' 


3161*216 367 43 56 


2120*031 


36i $6 JO 


^^F 


3 J 


3679-683 377 12 26 


33*8*578 


»7a J647 


^^L 


3 2 


4095-903 259 6 58 


5085-403 


352 j6al 


^^H 


3 2 


5686-703 253 7 IS 


S493»8» 


356 5^ 


^^H 


3 ' 


4045*352 268 24 42 


5097 7S4 


276 46 3S 


^^B 


3 3 


5511-906 3934846 


53»7"9S4 


30Z 14 6 


^^t 


3 • 


5389*438 375 S3 44 


6008*341 


373 »o 11 


^^H 


3 a 


4764-893 284 54 45 


5*39097 


a83 7 A 


^^H 


3 ' 


5538-700 264 31 44 


6949'! 13 


370 16 35 


^^B 


3 ' 


6297759 i74 IS '» 


7062-612 


365 40 51 


^^B 


3 » 


^1*9^19 A* ^S ^^ 


6549-376 


»«7 ja SJ 



Apr. 1907. F^i'sanal E(iufUv)n depending oil Magniiiidf.. 375 

lieiiuction of Hnliomet«T ttbgervati'ons. 

The approximate places of the etara for the Prpoch 1906*0 am 
qiiotvd iu Tabl« I. With tliesa approximnte places, tabuliir 
distasoes and poaition-ang]c» were computed. On cotii[iariD): 
these tabular distancps with the distances as derived frfun the 
heliometer mcasnroR wo obtain relations between the correctiona 
to the co-ordinates of the stare of the following fnnii,— 

S..(r + f Aa, - Adj) eo« 5„ din p„ + {dS, - AS^) coe ;>, = O, - C„ 
Sjjo- + (An, - Aa,) COB Sa ani /In + ( A^g - ASj) C08 p„=Of,- Ct, 

nhero the ituflixe« i, 3, 3 refer to the stars in increasing order of 
R.A., the suttjses a, b to the paira i-a. 2-3 respectively. S 
denotes the distance, ir a constAiit depending on the instrumental 
9cale-value, S the mean declination, and p the |)osition-angle of a 
pair, and 0, C respectively the oWrved and oonipiited distances. 
On eliminating it we derive 

+ {AJ;,-Ag,)"g/'"-(AS,-AS,)^^> = Q--^--Q^--g->. 



I. 



In like manner, from the olwervationa of position-angle introdncing 
a constHnt quantity tt tn dunuto the mean index correction to the 
positioii-civcle during the several "bservaiious nf a group, we form 
e<[uations of condition as follnivs, — 

S,«- + (Ao5-Aai)coBfi„co8j3^-(ASj-AB,)siti//„ = (0;-C;)MnS, 
S,»+(Aa, - Ao,) cos Sj cospfc - {AS, - Agj) sin jp* = (Ob' - C„') ein 8^ 

and on e]iii)inBti<~)n of r, S«,St being expressetl in seconds of arc 

(Ao, - A.,) °'"'^^'""j"" - (Aa, - ^<^r'\;^''p^ 

.(AS,-AS,)'''"''--.(A53-Ay^i^*=(o:-c;-iv-hc;).ini-. . . n. 

On eUiniuating AS^ from the equations I. and II. we obtain a Itoear 
relation between Aa, , Ao,, Aog, A5, - ASj, The al^'ebraio 
elimination is ciimliLTSume, but the riumerical elimiDation is easily 
performed in special ciises. This relation takes the form 

a(Aa, - Aa,) - j3{Aa, - Ao,) - y(A«, - AS,) -I- n 

r t?here, if the stars selected are well chosen, we have approxi* 
a<^^, while y is small in comfiitrisou willi either of Dir 
forming these etprntionn such n fnctor has beon introdno 
reduce the coefficient of Ao^ to unity, i.e. an IhaV a-v ^^^i 



k 



376 Sir David Gill and Mr S. S. Hough^ LXVil 6, 

The following are the equations of conditioa resQltiiig in this 
manner from the heliometer measures : — 



Equationa of Condition resuUing from Heliometrr J/eomres. 



Qroup. 
I 


0"433(Aaj - 4ai) - 0*566(409 - Aa-^) = +0-o65(a8j - 


-AS,) +0*29 


2 


0-508 


-0-492 


= - 0*025 


^0-53 


3 


o*455 


-0*546 


= -0*035 


+0-33 


4 


0-487 


-0-514 


= - O'OI I 


+0*25 


5 


0493 


-0*506 


= -0-035 


+0-17 


6 


0-468 


-0-532 


= -0-002 


-0-43 


7 


0-503 


-0-497 


= 000 


+0-42 


8 


o'S4i 


-o*4S9 


= +0*005 


-0-03 


9 


0-507 


-0-492 


= +0-015 


-0-04 


10 


o'547 


-0-453 


= -01009 


+ o-6j 


II 


0-519 


-0-481 


= -0*028 


-rO-U 


12 


0'4&2 


-0-518 


= -0x109 


+ 070 


'3 


0*499 


-0-501 


= +0-029 


* +0*65 


U 


0529 


- 0*470 


= +0-007 


+ 1-07 


'5 


0*527 


- 0*475 


= -0*017 


+ 0-23 


i6 


o'Soi 


- 0-499 


= -0-020 


+ 0-!l 


I? 


0-524 


- o"476 


= -0*034 


^o-.^i 


i8 


0470 


- 0-530 


= -0*018 


-o-io 


>9 


0'412 


-0-587 


= + 0-056 


+ 0-96 


20 


054s 


-0-454 


- -0-OI2 


+ 0-49 


21 


0647 


-o'353 


- +0*053 


+ 0-01 


22 


0-507 


-o'493 


= -0-015 


+ 0'OI 


23 


o'40l 


-0-599 


= -0'O24 


-0-44 


24 


0*480 


~ 0-521 


= -0'020 


-o-aq 


25 


0-553 


-0-446 


= -0-029 


-0-30 


26 


0-491 


-0-509 


= +0*013 


+ 0-39 


2? 


0559 


-0441 


^+0-037 


O"00 


28 


0-491 


-0-509 


= +0*043 


J o-i; 


29 


0-527 


-- o'473 


= -0-013 


-0*03 


30 


0-524 


-o'475 


= - o'ooS 


+ 0-09 


31 


0-556 


-0-443 


- +0*026 


+ 0-27 


32 


0-529 


-0-471 


= -0-038 


+ 0-32 


33 


0*499 


- Q- ^Ql 


= +0-020 


+ 0-6S 



Apr. I goj. Pergonal EqutUion d^ndituf on Magnitude. 377 

The quantities AS, , AS^ are retained in the right-hand luemberf, 
as in a few cases tht fiuully adopluJ valufsuf tlic declinations differ 
fmm those quoted in Table 1., which were derived from a fi-w 
early obicrvations only. The followiiig are tli(> correctioiiH derived 
from the incUtsion of additiDuai observations of the declination 
witli the Traiwit Circles: — 



Uronp. 
3 


At, 

-0-38 


AS, 

a 


18 


- 39 


-0-51 


19 


- 06 


i-os 


20 


- 16 


- ■!! 


11 


- '50 


' -30 


2S 




* -30 


3' 


- U 


- •« 


33 


-.. 


- -26 



III order to subject the magnitude pPTSOTiality to an aimlytiail 
treatment^ it wa^i now assumed that (?ach transit ohaervation in 
aOecltKl by an error which may be ezpreued analytically by the 
formula 

where m ilenotes the raugnitude uf the star and a, ji constants for 
the ohKcrver. The adopted magnitudes are those quoted in 
Table I. 

Thus for any pair of Htiint of R.A. Oj, a^ nay o{ magnitudes 
rrij, nij, the obiierved difference of K.A. may bu equated to 

or if we denote llila quantity by O and the tabular difleronce of 
R.A. u dependent on Table I. by C we find 

Aoj — Attj = - C - [a(7Bj - m^) + ^{'"i - m^{m^ + jUj - 8)] 

On Buhfltitutring the.'te expressiona iu the left-hand membere of the 
equations of condition resulting fruui the beliumeter meaaurafl, we 
derive a series of linear equations for the determination of the 
qiiantitiea of a, /? wliich may bo cxprcaatd in the fullowiiig tabular 
form. Th« siiffiiea attached to tliu absolute terms r*"'*-*nt the 
number of meridian observations involved in eacli. 



378 



Sir David Gill and Mr & S. Hoitgk, lx\1ij 



nrmip,. 



CoefllcieiiU of 



Aliaolnte temi* for 



l\>wcr. I'tui'l WllkUi. JtCfTk^ MuUli 



WO.-1 



+ 078, -0-43, 

+ :'o7a +0-39, 

■M-0«» +0-441 

+0-3^, +('371 +078, 

+ :"i6,j +091, -fO'4gj 



+o*i«i ... _ 

+078, -fl'«i» 

-o'ji, -016, -0*40, 

+ o-65j -Mxiti, -o-oi, +0'36j '4-0*54, ~0'49i -04ft 

+ 1*28^ +o'57j +i'i8, +0-39^ ,.. -01% 

+ o-a8, +I'I74 +0-20^ ... +ox>7, ,. -o'sj, 

+ 0-66, -i-i-oS, -t-o-lSi OfJC^ -o'56, .. ^ ox», 

+0-274 +i"2St +0*9. +o*09i +o-54ft +0-07, +oxi^ 

+ 0-»j +0'83j 

+ o*8«:^ +l'07a +"'8oj +019, -0*41, -0-195 +0*1 

+ 1054 +i-42« ^ 

4o-6i^ f03i, +008, +0*44, +034, +o-lOj -o- 

-0*19, -O'lOi, 

-0-134 +024l -OM2, +070, +003, +0-62, +0 

+ 0-664 +0*9) •- +o"50i +ox>2, +o'o8ii +0 

+ 0734 +I"Mj 

+0-23, +014, +o-5Sj -o'4Jj +o-K)j +o-aOfc -o-»' 

+ 0-244 +0-29, 

+qi3j -027, +o*33i Ho-iQ, -0-298 +o-i5g -o-oi 
-o-iS, +0*28, 

+o*444 +1-03, +0-3S, +0-4P, -o-ai, -o*a6i +o•a^ 
-o-ag, fo-54, +0-304 -o-ai, +0-28, +o-io» -o*a3, 
+ 075, ... +006, +o'42, +o*ii, -0-03, +o-2i, 
+ 0*25, +1-14, -o-ii, +o-iO| +049, -0*17, -o 
-0-09, ... +0-13, -0'»3, +0-6&, -O'll, 
-019, +1-33, +oio3a +0-48, -0-22, -010^ +0 
-1-89, +1-13, -005, +101, +0-49, -o-is, +.0 
+0-76, +2-01, +o'i6b -o^J9, +079, -0-05, +o'xi, 
+ 2-OS, . . -oao, ... +0-07, 4-0-3I, +0-24, 
+"76, +o'3i, +i-oa, +0-33, +0 



I 



For tli6 [lurpoKe of combining; tlieso oquations, it Mra« m«saai. 
tli&t the errors in ihu absolute terms resulting from the keltotaeler 
measures were insignilicaat <-«ra[)arcd witb tbo.se resultiiij^ from Uw 
tiuBKit ob&evvatii->i)8, and thn e()imtioii9 were accordinglj waiefa|«d 
accortling to 1\ib namXiat ^s^ i4tvw».\« (jV»*.x-sw.\,\<«va n( each nou 



I 




,Apr. 1907. Personal ISqualioii de^mtdiiuf oti MagnUxkde. 379 



obtained by tbe meridian circle olwervers. A least squan solutiuo 
then led \v tlie following results : — 



Prot«i>l(r error <if 



Obanrvv- 


In arc 


iDiimo, 


In Mc, 


PoWtT 


^0-134 


■ 


-0*O20 


Pea<) 


^ 148 


+ 0099 


+ •Oil 


Wilkin . 


+ 117 


+ -0078 


- 018 


JefTnes 


- -053 


- 0035 


+ twS 


MalliR 


+ 'Oil 


+ 'OOOf] 


+ -oio 


\\a<»\ 


- -015 


- 'OOIO 


■f '006 


Jacksoii 


- -003 


- 'ooua 


+ '006 



In ItDH). 



+ 0007 ± -0016 ± 0005 
- "0012 ± ■0011 ± 0003 
+ '0019 ± '0027 ± -0007 

h '0007 ± ■cx>23 ± '0006 
+ txxH ;b '0016 db 0004 
+ '0004 ± "0025 ± 0006 

The reeultiiig corrections to the observAtioQs tu mako all 
spotid with thniie of iitara of tho Tonrtb Tnas:tiitnde are eb 
^foHowB : — 

CorrtetiCH Jbr Peraotud Equation in ILA. depatdijig un Magitittuit. 
Mac fower. PMd. Wllkln. JcffriM. MnUla. Woo<l. JftckMn. 






+0-0S7 


> 
+ 0*029 


+ 


■ 
o-oso 


-OTOM 


-0*007 


-Ot>10 


■ 
-0-007 


I 




2» 




M 




34 


27 


4 


7 


4 


3 




23' 




17 




21 


14 


1 


4 


2 


3 

4 

s 


+ 


"OlO 


+ 


W9 


+ 


W9 


- -oos 


000 


- X»l 


- •OOI 


- 


-008 


- 


•oil 


- 


•007 


+ -oos 


- "002 


- "OOI 


000 


6 


- 


13 




25 




It 


000 


4 


000 


- -OOI 


7 


- 


t6 




36 




11 


- xmti 


8 


- "OOI 


- -003 


8 


- 


'S 




5' 




la 


- 16 


- '3 


- "OOZ 


- -006 


9 


- 


"4 


- 


•06S 


- 


\)09 


- "029 


20 


- W5 


- 009 



The qiiaiilities thus derived in tint cosu nf tbe observers who 
used tbe travelling wire method appear to he qiiit« insigiiificanl 
except at the extreme limits of magnitude invt>lved m the t.ab)6. 
The strength of tbe determination at these limits depend^ how- 
ever, nut »o Diuch on the actual weight dorivt-.j directly front tbe 
rtbeervfiTiions, as on tbe Wfti^ht artificially extended U» It by the 
URamption thai the magnitude personality may he exprestiad by 
the foTTDula aiii + fim^. 

The iiKe of such a formula can only be justified as a convenient- 
means nf iuter|Kilation ovor ttie range of majiuitudf t-nvercd by 
stars ocLuidly observed. If we limit ounielveg to thn range ' 
within which ttmits tbe majority of the ptar^ are cotitiun 
may safely conclude that the observations dealt will 
evidence of tbe existence of sensible personality d 
magnitude. Ileyond thoM limits the quantitieA ar 
than might reaaonnbly be expected to arise itM-Ok U 



L 



380 



On the Vtxlue of the Solttr Pamllax LXViL 



It I 



empiru-al *uxtra()olatioa' formuU. wbich will have the e&ot li 
ma)|^)f>'ing the nccideniAl erront of ohservatlon at the extremiUai 
of tho utble. 

The resnlt* for the obgervers witli the old Traasii Cireir (n« 
oWurvaLinns made i>artly tbrongh vcreen* In 1900 and 1904 ma 
follows:— 



Mag. 



PMd. 





• 


ft 




+ 0-008 


-*■ 0-037 




7 


2S 




5 


iS 




4 0-003 


■f- -009 




... 


... 




- -DCM 


- -009 




9 


- oiS 




- 15 


- -026 




31 


- *034. 


9 


28 


•043 



The agreement with the present results is as clou as could b* 
expected, except in the case of the briKhtcr stars for Power tad 
the fiiiiiter stars for P^ul. The ilisirorcltiiicoB ore doubtleaa doe v> 
the iuudequauy of tlio material employed to corroctly det«rmui« 
the m<i^uiiiide i>erHoiiaHty at the^e extreme limits of uiagultnilc, 
rather than to any real change in the ohsprver'B liabitn daring tlit 
interval between the two eels of obserrations. 

TbK plan of these observatioiut was prepared by Sir iJaTkd 
Gitl, and the observations were well advanceil before his departan 
froiJi the Cape. The obserratintis were completed and the cvn- 
putalione made ^nd prepared fur press in tbeir present form undq 
the direction of Mr S. S. Houjth. 



On the Value of the SoJar Paralinx remUing /rom 
Oreertwich PhotiM/raph* nf JCrov, 1900-1901. 

{Ct/mmu»ieaUit by (A/ Jstrononur JSoyn/.) 

The disctissiuu of the photographs of Eros taken at Grveniri 
dnring the oppi>»itiou of 1900-1901 liaa now been completed, 
a Talue of the sol»r purallax buH been deduced as resnltiag 
the jibotugntphs taken ut Greunwich, The plan of tbe 
Comoiissioii i:onteinp]at4id, ultimately, the combined diacaasion 
the photographs taken at all the co-operating obRervutiirieiL 
there is obviously >!reat ditliculty in tn^ating such a man 
heteruKeuKous matt-rlat, and it seenia desirable, in the firttt tnstai 
to diiicusa sepanitely tho ubourvations of tho individiini observat 
aud deduce a value ol tihe miW \iB.'c«.VVkX vc^ %acb caae. 



Apr. 1907, from G-reenwich Photoi/raphs 0/ Eros. 



381 



With this view the reaults obtained from the Greenwich 
phutograjjljH arti ht-rc' ^^ivurj. There wtrti in all 197 photoginphs 
taken with the A9(ro{;ra)jblc 13-iuch refractor ami 153 Ukeo witb 
\t\iii ThomiiAiiii 26-iiich refractor Utween 1900 October i and 1901 
KebruHry 25, but fur the determination of the solar parallax the 
diacuiuiion hm hven confined tu the period from 1900 Octol>er 14 
to 19D1 JumiBry 18 (151 photographs with the Afttrugntphic and 
103 wiUi the Thoiiipsuu), the oiaterial before aud after these dat«8 
Dot bcin;^ suitable for determination of the solur parallax, though 
useful for the positinn of Kros. 

It niAy be recalled here that, a» ejcplained in a paper cm tha 
"New Greeiiwicii micromecer for measurement of photographs of 
EroK " {Mimt-My NotU-e^t vol. I.\iv. p. 633), ten to twelve " roforcnco " 
stars and six ''cumpariHun" stars were measured with Eros on each 
Atttrograpbic photograph, and the resullA from the^ie two selit of 
Stars to wbi<;h Eros wae referred have been discussed separately. 
Thu "reference" stars setei-ted fruin M. fjiiewy's list wjlhiu 55' 
of the plate centre are alL brighter than ninth magnitude and 
therpfore brighter than Eros, The "t:oni|iari*Dti" stars, on the 
other hand, are of a]ipri>ximatf ly the same brightness as the 
planet and within 25' of ilie plat*? ecutre, bo uh to Iw well within 
the field of Uie Thumpeon plateti for which they served as poJuta 
of reference. 

Tlin d(> termination of the movement of Eros in the interval 
between the groupB of photographs ci)m|>arerl, which is ei^sential 
£or the deductiou of thu parallax, was lirst undertaken. The 
measured pottitions of Kron were compared with tabular places 
im M. Millosevich's ephemerides (Astrographic Conference, 
Circular No. 9), uaing the value 8''8oo for the solar parallax, 
which wa« a sufticient appruximatioa for this purpose. The 
change of error of the ephemeris during the interval bptwecu the 
groups of obsorvatioiifi to Iw compared fur parallax was generally 
considerable (amounTing at times tu "'lo per 'fay), but it cnuld bo 
determined with great accuracy. The meaua of gruups r.f measnred 
(K>sitioQs of Eros were taken so lis to give the vrror uf thu ephemeris 
at int«rv(tls of about live days ; froui these Itm errur uf the ephemeris 
vas represented by a smooth curve, which represented the obser- 
vations very sausfactorily. 

The correction to the adopted parallax was derived by compar- 
.ing oltsorvB lions at different hour-utigle:). It was not u))ua)ly 
'.desirable to make comparisons between groups of observatm"" 
'separated by an interval of more than one day, owing to the 
accidental errors introduced by errooeons places of the at 
which Eroii was referrL-d. The same reference and l-oi 
stars were used tluou^'bout oo^'h night, so thai in ded 
parallax from comparisons between phoLngrapha tok 
evenmg and the following moniing errors in the sta 
«Uiniuatcd; but in all other com)>ariiii>iKs some of lli 
are different for the two groups of plate«, and tl 
interval the weaker the connection between the tttar-p 



3S2 On the Value of the Solar Parallax lJETa< 

From a discussion of the RujJU A$femum» the foUowtog r 
have been derived : — 

Sviar ParaOait. 7*tonti^ 

Aitroj^phie photograithn, BrferrDDe SUn, S'793±*005 J97 

„ „ OonipMTiHon Stars, S'8o9i: -0052 397 

Tboiiipson phMoj{nphi, CinnjMriiioii SUni, 8'Soo± '0063 31-9 

Oombined iliwniBsioQ uf A«triiyri[ibk snd 
Thompoon photogrnith*. Oompnrisnn Surs, 8'800 ± *0044 /i*' 

Tiic unit (if weight used bcre in the weight of a coinpartson l«- 
twevii ono niantiiiK uiid oitc evening pliotuurapb under jnttuaHj 
the most favourable conditions, viz. when Kros undergoes k pwit- 
lactic displacement of 35' between the two plates. 

The ditferunce between thy resulta derived from tho K«f<>rnm 
and Cdtnpiirimm Sturs is of a. sjstvmatic character. It ia found Uut 
if pliLtf'fi taken at a large hour>angle are compared with thorn iaXtt 
near the meridian {on the same ni^'ht and with the t«le«co|>c on thf 
same sid<4 of the pier), the compftrison stars are dinplaced relattfrh 
to iliti refereuce stuni, always tn thu same ilirectiun and in th« meaa 
by about '07 in K.A. It is not clear whether this diBplaouDfOt 
(iepeuiU on liie cotiiparwon ^tarft baini,' fainter thuu Ihe referract 
stars, or their bein^ rearer to tlie centre of tha plate. In eitJi*r 
i-Rse we must hu(i|H]vu tliut y.ro» beliaveR like the comparison tx*n 
ratlier than like the refcreucQ stars. For that reason •tnl/ tbt 
results from the comparison stars are usi-d in "btnining the fioii 
value of thi- |Mir>illfl.y, It »^houM he notic<.-d that uo ditninutioo d 
the accidental error would be obtained by taking the mean uf tli* 
_ra»ulle of thu c-ompuriijoti and icferouco stars .: for the two dete^ 
inatiuDB are not independent as regards accident'il error, dependin*:, 
'b9 tliey iU), on the Kunic measures of the imajjre of Kro8. 

Tho clcHse ngn-ement between tho results derived from Ihi 
Astrographtr. and Thompson plmtographs (Comparison irtant), airi 
the fact tliat tiic same star-plu<:es were used m the two raaea, seMDfi) 
to jnstify a combined discu&^lun of their results, reiptrding the twti 
sots of places as homogem-ous. There iva* a considenble gain la 
thuFc treating them together, as the two instrnmentti had eapplfr 
mented one another considerably. In this discussion, conipa: ' 
exlotiding over mort; than a day were rigorously exclutled. 
rostUt given abovo mimt be regarded us tho principal cunrluai 
the whole investigation. The results of the separate comiwriaii 
are Kiren in Table I., at the end of the paper. 

Without muuh [0^^ of maUjrial, the disctiasion could be rt' 
arran^ftMl, so that ci'mpari^ons were only made between the t-veoi&it 
and following morning ohHervations. A very considerable redactKS 
in the probable error {inferred from the diBCordancos) took pfr* 
(notwithstanding the loss of material), owing to the oliinixutioB «( 
erroneous star-places. A comparison was also made between tbi 
morning and following evening obRervatioi»«, the probable 
this case being mon ib&n twice as great 



riani^J 

ion«H 
tiaiia^l 



Apr. 1907. froM OrtentifvA PKotog^-aphs of Bros. 



383 



AMHpaMi owl A^ragnrktt OomA^miI. Wti$>>l, 

Brentng to Uoming compftriMnt onlj, 8'8o7± "0036 $8*5 
Monting to Br«ning compariaoos only, S'Sot dk t>o8o 35*4 

The probable error for unit weight of ao evening to moniiog 
teoEuparison in + 'gzS, and for a momiitg to evening comparison 
LIB + '-048. The greater port of thi« difference in the respective 
■probable errant niu&t be attribtttod to tbo errure uf Dtur-placea^ 

In a formiT |>a[»er, "On tho errors of a photographed rt>8caa" 
\{Mont.hhj yotire*, toI. Irvii. p, 175), it haa been shown that the 
[dJvixiou errors of the central lines uf the ri-seau between which Kros 

{alls affect !>y»tetniitica11y the deiluced value of the solar parallax. 

Detaihi were there t;ivon of the determination of thoae errors. The 
loorrections there deiloced (additional to those which had heeii 
Iproviaionally employed), amounting in the mean to +''065 for 
[Aatrographic photographs, were applied to thu poeitioDS of Exo» 
[l>efi>re deducing the preouding re.suU«. Thia qmuitity was very 
I closely continued by a discnsstou of the residuals of the oomptiri»on 
l«tar*>, which indicated +'*o6S. The probahtt* erroi* ttf tin.' two 
[TesaltB 8e|ramtely are, however, about ±''006 and ±'*oo8 rvspeo- 
,tively. lu order that the effect of the uncertainty iu tlie deter- 
imination of division errors may be estimated, ihe resultti obtaineil 
['before these corrections were applied are given hnlow. 

Prrtvitional Hatutlt uncon-ected /or Rtn'tiual CHvigion Error. 

A»trof^t»liU* |iliotAgr»ii>ts, Ri!fflreiic« Stars, . S758± '0054 

„ ,, Coiiii«rt»OM 8l»r«, 8774±-O0S9 

Tbauipson fl*802± ao?* 

It will be seen thut the result from tho Thompson plxito^rapUs is 

practically tin&ltered by the applicalion of the new division ernirs. 

'I'hifl is due to the fact that, in the first plare, thti imulf of the 

[Thompson phologrupha is twice that of tho iVstroyraphic, and that 

fiho corrections for division error urw consequently halved. Further, 

'the accidentiil variations in the position of Kron relatively to the 

'linns of the r^Ueau were much greater tban in the AHtrographic 

, photographs, and during pnrt of the •■ppoeition (be tvseau was not 

reversod whc-ii tbt* telescope {lassed from K to W of tlw pier. For 

Astrographic photographs the application of the divisiou correction 

'-065 haa increased Uie deduced value of the Mtlar parallax 

A discussion was also made tuing only eomparisoni between 
[nlatca taken with the telescope on the aame aide of the piar, u 
[that the diviMon error of the n^aeau waa eliminated. 



Ttittetiyr B oUy. 

ABtrogn[)hio raTerence iit&rB, 
„ oomiaritas „ 



Sdar FartUtMt. 

878i± 009 



384 



On the Valm o/the Solar Parallcuc utTO 



The weight of t\m determtiiatioD w smaU, a large i^ior: oj Urn 
mat«riEl beiug wasted. It, how»?ver, shows very markedlj' lie 
di)Ii;rencc Iwtwoon tlie reference and compariiw»n stars. 

From the DeclinatuynA of KroB the folhiwing ralnn *r» 
obtained : — 

ARtrofcraphic photognphs, ivferance Btan, 9'7fi3±'DJff 7'f 

„ ,, comp«riNOri ,, 8'St9±^l4 7't 

TUomiiBOD pfaDtofn'ii]>lis ,, S78j±-oi6 5-3 

Mean (oom|MrisoD stani), 8'8oi±'Ol6 

No epccial determihation of the division errora nf the c«nSnl 
liiiea of the rcseau was ueedtfil fur the docii nations. The paralUl 
being of t)ie sutul^ sign on both tfid'Oa of the meridian, compariMDi 
were made betwet^n |:ilati>n tatcQii at a hirge hour-angle G or VT 
and those near the meridian. About the same proportion of In» 
plutes were taken with the telesoopu K and W (reseau direct and 
reversed) aa meridian plated ; accurdingly the value of the divatot 
error of the central lines of the r&ti^an do'!8 not afTrict sydt«maticallf 
the deduced pundlax. The method employed for deducin;; tbt 
parallax was to divide the obBeivalionH into groupij, each exteodioc 
over Lwu or Uircu days, and oolve eucb group suparately \rf Icait 
squares. The r«-sultN from the individual groapa for Asiroj^npbie 
Comparison Stars are given in Table II, 



Tablr I. 

Right AactnMuma. AMrognpikie and Thompton combined. 



Dktc. 


No. o( P1»tw 


DiBinvDiM) 
of PanlUi. 


Wvlitht 


t« Solar PU»Uu 


1900, 

Oct 14-15 


4. 1 


10 


•3 


-%M5 


., ao 


3. ' 


n 


■4 


-117 


21 


4. z 


23 


a*3 


+ XCff 


.. a6 


6,4 


25 


4-8 


-*• -006 


.. »7 


5.4 


25 


4-5 


+ 1038 


,. 28-39 


a. 5 


36 


3'i 


- 1009 


Nor. S^ 


3, 3 


19 


fX 


- ^Oll 


1. 9-10 


3.3 


27 


35 


+ •Oil 


., 10-11 


2. 3 


27 


2« 


+ X>l« 


1. n 


5.5 


28 


6-3 


- v>ii 


.. 14-1S 


3. 5 


24 


3'5 


-'067 


.. M-a3 


4, 5 


28 


5-« 


+ t»9 


.. V 


5.4 


15 


1-6 


-•oos 


Dm. 6-7 


9. 3 


t6 


I '9 


+ •054 


., 9-»o 


i,i 


»S 


v% 


+ -011 



Lpr. 1907. from Greenwich Pkotogi'apks of JSrot. 



38s 



Date. 



No. at PIftUa 
oomiMivtl. 



Tahle l.-~eontinu£fi. 



6,3 
6,6 

5.5 

Z. 6 

3.3 



DtHcreocs 



21 

a? 

13 



2-8 
6-5 
5*0 

3-5 
7 



Carrtetlon 
toSotuPiralUx 

- ■<M4 

- -018 
+ x»3 
+ 033 
+ ■033 



5 4.6 la rt 

8-9 7,4 18 2*6 

13-14 6. 3 22 3-4 

15 5. 5 » 3'^ 

17-iS 2,3 iS 10 

Ueaa Oomctioa + 'ooo± -0044. 



The weight w given hy the formula 



smn 



^M' 



'OOO 

•oSi 
+ •030 

+ •034 
( t -277) 



where m and 



' -n are the uumbui'S of platea in the iwo groups compared, and Sw ia the 
dilTerence of parallax of Kros between the two groups. No plato 
is used twice over; i.e. if an evening plate is compared with plat&f; 
taken on the preceding raorniog, it is not alao compared with 
thutfc taken oit Lhu nucceediu^' iriurtiing. 

The discordant rcsalt for Jan. 17-18 has been lejeetfd, as there 

lar« Reveriil unsatiAfoctory ciroutnAt.iincea in thB Thon]|iAnn photo- 
graphs on which it depends. On four of the five photogriiphs the 
imagwt of Eros were noted as dirticult to measure, and furthnr, 
ditTerent referencs stars had to be u^ed for t]ie two days comiared, 
thus introducing the errors of the ebar-pkces which depend on 

f visual obeervations alone. 

Table II. 
DtdinatioTts. AMtroffrapAwfmm Comparitim Stan, 

PmnUlax. 




386 



Messrs Coweli and Crommeiin, 



Lxra& 



Tablk IL—CMUinuai. 



tat*. 


WwtghL 


Oomrllnti W) 


1901. 




■ 


J«n. 4-5 


'4 


+ 060 


.. 8-9 


*4 


■040 


.. "4-15 


•2 


- "100 


Mmq Oormtinn -f 'oi9i:x>l4. 


Bof/tU OlUm'oiin^/, Orrmwieh : 




1907 April 9. 







The Perturbations 0/ ffall«i/s Comet. By P. IX. Coweli 
and A. C. D. Crommeliu. 



( 



Thfl differential equatiuiis of vMriatioii of the four plemfuli^ 
n, e, CT, c, the mtaa molion, eccentricity, luuipmde uf pmibelm 
and ciMrth are — 



1 
m' 

1 
m 

I 
m' 



n 
edzs 






A[rf*-c/CT{i - V(»-^')J'=^(«''XJ«)+«,(a*yrf«) 



f — sin u cos n - e sio ■ 



3<! COR It +-«■'< 



f,= 2V(i -ff2)^ -ainw + <iinn 



V(' 



>vbere 

3 sill u 
— J{i -e*)ain « coeu 
~ J(i ~e'^){i - PC03 u + Btn*i(} 
2{ — co8u + e(l +cOs'u)-*r*cysw| 

vhero m'X, m'Y are llie oom|K)iitiuI« of the duturbing foroe, tbt 
axes uf j^, II being drawn in the plane uf the orbit towards perihtilxD 
oud [lariillfl to the minor axis reepectivelj. 

The (]Ufttititie(i n„ etc^ are functions of the ecuentricitv «, ud 
the eccentric anoiufi]; u only. They are tabulated in Tabte I. (or 
every odd degree of u, nnd fur ibe value ^/(I —«')<= •25400a « 
« = *967z04. It iH clearly unnecp.sBary to talttilato beyond ■* iSo". 

All quantities iu the above equati<m» — , etc, n„ etc., a-X^h, 

It 

etc., UB pare numbers of zero dimenaioiu in space and tiiun. All 

nference ti> Huch arbitrary units as the Earth's mean diatonaa^ 

the mean si^lar day l» thereby avoided. 

The tirat part of Table I. gives tlie comet's j ami y co-ordinsW 

divided by the semi^miyor axis, and also n/, the coxnet'a 

anomaly iu c\rcw\at myuautw. 



^LApr. 1907. The Perturbations 0/ Halley's Comet. 


3S7 1 








Tablk I. 








^ 




Fir$t and S(»a»id QuadratiU. 


Unit = oxxiooi. 




^M 


^H » 


V 


nl 


tW-Hl 


u 


c 


► 


nl 


vr-nl ^1 


^H a 


« 








a 


a 




■ 


B 3K 64 + 4 43 


57 


6282 61 


* 

9< 


- 984 66 +253 96 


621 19 


5661 99 ■ 


H31 43 


13 =9 


I 74 


62S1 44 


93 


1019 54 


253 65 


657 28 


S^>25 91 ■ 


■ 3899 


22 14 


2 97 


62S0 22 


95 


1054 36 


253 03 


694 54 


5588 64 ^ 


■ as 34 


30 96 


4 30 


6278 SS 


97 


1089 07 


252 II 


732 9? 


5550 21 


■ ao 48 


39 73 


578 


6277 4> 


99 


1133 64 


250 87 


772 58 


5510 60 


H 14 43 


48 46 


7 44 


6275 75 


101 


1158 01 


249 33 


813 35 


546984 


■ 7 <7 


57 M 


9 32 


6273 87 


'03 


1 192 t6 


247 49 


85527 


5427 91 ^ 
538484 ■ 
5340 62 ™ 


■ t 28 


65 74 


II 47 


6271 72 


105 


1236 03 


245 34 


89835 


^B 10 90 


74 a6 


1392 


6369 26 


107 


1259 58 


242 90 


942 56 


■ 31 6S 


8269 


16 72 


6266 46 


109 


1292 77 


240 16 


987 90 


5295 28 


■ 3362 


91 02 


1990 


6263 28 


iti 


1325 57 


237 '3 


"034 35 


5248 83 


■ 46 70 


99 »5 


23 5' 


6259 68 


113 


1357 94 


2338. 


loSi 91 


;20i 28 


H ^ 9° 


'07 34 


27 57 


6255 61 


"S 


1389 92 


230 20 


1130 54 


5152 64 


H 76 so 


115 3r 


32 M 


6251 05 


117 


1431 19 


226 32 


llSo 25 


5102 94 


■ 9:158 


133 14 


37 24 


6243 95 


ng 


1452 01 


222 15 


1231 01 


5052 18 


HlID 04 


130 82 


42 go 


6240 28 


121 


1482 24 


217 72 


1282 79 


500039 


■12853 


138 34 


49 18 


6234 00 


123 


151 1 84 


213 02 


'335 59 


4947 60 


■148 05 


14569 


56 lO 


6227 oS 


"25 


1540 78 


2o8 06 


1389 38 


4893 8t 


■16857 


152 86 


6369 


6219 49 


127 


1569 02 


202 85 


1444 12 


4839 06 


^■190 06 


15985 


72 00 


6211 19 


129 


1596 52 


197 40 


1499 S3 


4783 37 


■ai2 49 


166 64 


8t 04 


6202 14 


131 


1623 26 


191 70 


155* 42 


4726 76 


■>35SS 


173 23 


90 86 


6192 32 


133 


1649 20 


185 76 


1613 92 


4669 26 


^■960 lO 


179 60 


toi 48 


6i8i 70 


<35 


1674 3> 


179 60 


1672 sS 


461a 91 


■flSs 31 


i8s 76 


M2 94 


6170 35 


'37 


1698 i6 


173 23 


•73' 47 


455' 72 


■311 14 


191 70 


125 as 


6157 93 


'39 


1721 91 


166 64 


1791 46 


4491 72 


■337 ss 


197 40 


138 46 


6144 73 


141 


1744 35 


159 85 


1852 23 


4430 95 


■ 36s 39 


20a 8; 


15258 


613a (iO 


'43 


1765 84 


152 86 


I9'J 74 


43<'9 44 


■393 63 


208 06 


167 64 


6115 54 


"45 


1786 36 


'45 69 


1975 90 


4307 22 


■^256 


213 02 


183 67 


6099 51 


147 


180S 88 


'38 34 


2038 86 


4244 33 


■«SS i? 


217 72 


zoo 69 


6082 50 


149 


1S3437 


130 82 


2102 39 


4180 79 


■4^ 39 


222 15 


3i8 72 


606447 


'51 


184 1 82 


123 14 


2i66 54 


4116 65 


■513 21 


226 32 


237 77 


6045 41 


'53 


1858 21 


"5 31 


2231 25 


4051 93 


■V4 59 


230 20 


257 88 


602s 31 


'55 


1873 51 


107 34 


2296 50 


3986 68 


■576 47 


23381 


279 06 


6004 13 


157 


18S771 


99 25 


2363 25 


3920^4 


■'<6oS 84 


»37 '3 


301 31 


5981 87 


"59 


1900 78 


91 02 


Z428 46 


3854 73 


■641 64 


240 16 


324 68 


5958 5> 


161 


1912 72 


82 69 


2495 09 


^,^ 


■ «74 H 


242 90 


349 15 


5934 04 


163 


'923 ii 


74 26 


2562 r 


^^BB 


■ 708 3S 


245 34 


374 75 


590841 


165 


1933 >3 


65 74 


2629 


^^^^1 


■741 2$ 


147 49 


401 49 


5SS1 70 


'67 


'91' 57 


57 M 


r 


^^^^1 


■77640 


»49 33 


429 38 


5853 81 


169 


1948 83 


48 4^ 




^^^B 


■ 810 77 


250 87 


458 42 


5824 76 


171 


'95489 


39 




^^^B 


■ ^5 34 


2p II 


48863 


5794 56 


173 


1959 75 


30 ' 




^^^B 


P^B>a OS 


253 03 


520 01 


5763 t8 


175 


1963 40 


31 




^1 


f 914 87 


3S3 65 


552 56 


5730 63 


177 


1965 83 


11 




^^^B 


t - 949 75 


+ 253 96 


S8629 


5696 90 


179 


-1967 OS 


■V* 


^ 


J 



^H 


r 




1 




^ 


^L 


388 


Meear 


8 Cof^ Cromimlin, 

i 


J 


^^^^^^^^^1 


I 






CnmeUao to 




^^^H 


p 


First 1 


(M"* 


FnnllAX. 


H 


^^K 


"4 


Wj 


*m 


+- 060 


^1 


^^M 








- -040 




^B 


+ s* 36 - 1 13 


-844 


- 2 15 


- -lOO 


^^^^1 


H 


157 01 3 37 


9 30 


2 14 




^^^^1 


■ 


361 47 5 60 


11 19 


2 12 


♦4.. 


^^^H 


■ 


365 61 7 80 


13 93 


3 03 


756 A^ 


^^H 


H 


469 30 9 97 


»7 57 


1 83 


7S2 62 




^H 


572 43 " oS 


22 09 


146 


74* 00 


n^^H 


H '^ 


674 85 14 14 


2748 


- 083 


742 47 


'^V 


■ 


776 46 16 13 


33 72 


+ 17 


73604 


16^ 


■ 


S77 12 18 04 


4078 


164 


728 70 


16 42 1 


I 


976 70 19 86 


48 64 


3 7i 


720 48 


16 5) 


H 


1075 10 21 5Ji 


57 27 


652 


7" 39 


16 67 


H 


117a 19 3j ao 


66 64 


to 24 


701 42 


16 .M 


■ 


1267 86 24 71 


76 7> 


•5 03 


690 6t 


»r 33 


■ 


1361 97 26 10 


87 46 


21 06 


67S95 


17 86 


1 


MM 43 27 3b 


9883 


2853 


666 46 


18 56 


■ 


1545 II 2« 48 


110 80 


37 62 


653 16 


ly 46 


■ 


1633 92 29 47 


123 3» 


48 54 


63907 


20 38 


■ 


I7W> 73 30 3< 


136 32 


61 50 


624 19 


31 96 


I 


1803 44 31 ot 


'49 79 


76 7» 


608 56 


23 60 1 


■ 39 


iS»7 96 31 55 


163 67 


94 40 


592 iS 


»5 5& 1 


H 


196S iS 31 94 


"77 93 


114 76 


S7S •19 


37 86 t 


1 


2046 00 32 tS 


192 47 


•3803 


557 29 


l^ 52 1 


■ 


2:21 32 32 26 


207 28 


164 42 


53882 


ii 57 1 


1 


2194 06 32 iH 


232 31 


194 "5 


5i<i 68 


37 05 3 


1 


22*4 13 31 94 


237 50 


227 42 


499 92 


40 98 3 


I 


a33' 44 3' 55 


252 8q 


264 44 


479 54 


45 38 1 


■ 


'395 9" 31 01 


268 16 


305 41 


458 58 


SO 30 J 


"55 


2457 46 3« 3' 


2Ji3 S3 


35° 5' 


437 06 


55 74 J 


57 


2516 01 29 47 


298 86 


399 94 


415 02 


^i 74 3 


59 


2571 50 28 48 


314 09 


45384 


392 46 


68 3J 3 


6i 


3623 86 27 36 


329 ao 


5'2 39 


369 42 


75 49 A 


63 


2673 o2 26 10 


344 " 


575 72 


345 94 


83 29 4 


65 


2718 92 24 71 


35S81 


<M3 96 


322 04 


91 72 4 


67 


2761 ^ 23 20 


373 23 


/I7 23 


297 74 


too Mo s 


69 


2800 74 21 58 


387 34 


795 61 


273 oS 


"0 54 5 


71 


2836 56 19 86 


401 10 


879 [8 


248 08 


130 96 6 


K 73 


2S6S 91 18 04 


414 46 


968 00 


222 79 


132 06 6 


1 '' 


2S97 78 16 13 


427 40 


1062 II 


197 21 


143 Ss 6 


1 7' 


2923 11 14 14 


43988 


1161 52 


171 41 


•S** 33 7 


■ 79 


2944 8S 12 08 


4SI 88 


1366 22 


"45 40 


169 47 71 


^_8i 


2963 06 9 97 


463 35 


1376 >9 


119 20 


'^3 35 ^ 


«9 ^ 


2977 64 7 So 


474 29 


i49> 39 


92 86 


197 8y &. 


^'f 560 
299^*9 3 37 

h2099 5->'' ' ^^ 


48466 
494 45 


1611 72 
1737 12 


66 41 
3988 


21J II 8! 

228 98 91 


-50164 


+ vtei a^ 


- ^1,^ 


'*-**.\ -a* -ij 


J 




^^^^ 


■- 




-^^1 



^.1907. r'** 


PeHt'-rWions of R-^f HaUeys Comet. 


389 1 


^ 




T«)LE L 


imtiiiugd. 






^ 


^P Pint and Stcmd 


Quadntnb. 


Unit = 0*00001 


, 




^ 




ni n* 


-M 




% 


•y 


w„ 


•• ■ 


^b 64 ^ 4 4i 


57 62SZ 61 


55 


+ 13 30 


4-262 6$ 


-984 5J 


-51650 ■ 


^K 43 13 ^ 


I 74 62Si i -^^ ^ 


3988 


380 41 


iO)8 14 


53*98 ™ 


^P 99 " I** 


a 07 6'" 


. 2386 48 


66 41 


298 75 


1050 35 


548 73 


K 34 30 96 


4 ,-. ^7 


2434 89 


92 86 


3>7 65 


loSo 96 


563 65 


K 48 39 73 


S40 aa 


^587 30 


119 30 


33708 


1109 80 


577 66 


K 42 48 46 ** 


545 63 


2743 45 


'45 40 


357 00 


1136 74 


590 70 




550 4» 


3903 07 


171 41 


377 38 


lt6i 60 


602 68 


Bx zS 6c'^ '3 


554 57 


306587 


197 22 


398 18 


1 184 25 


613 52 


^■h qa '^ °4 


sss '» 


3231 52 


222 79 


419 S7 


1204 54 


623 18 


■b6S -^ >9S6 


561 d6 


3399 71 


248 08 


440 89 


1223 34 


631 57 


^E 63 '< "^1 SS 


563 42 


3570 07 


373 oS 


463 70 


'237 53 


63864 


^E 70 S^ ^3 :»> 


565 »i 


3742 24 


297 74 


484 76 


1249 99 


644 34 


^K ^ 92 24 71 


56b 46 


3915 85 


322 04 


507 02 


1259 61 


64S60 


^K 2J 02 26 10 


567 18 


4090 49 


345 94 


529 42 


1266 29 


631 38 


^E ^3 ^ 27 36 


567 40 


4»6s 75 


3''>9 42 


55' 91 


1269 96 


652 65 


^E 71 $0 2& 48 


567 15 


4441 23 


392 46 


574 44 


1270 53 


652 36 


H|^I6 01 39 47 


566 46 


4616 50 


415 03 


59695 


1267 94 


650 48 


Hi457 a6 30 ji 


565 3S 


479' 'o 


437 06 


619 38 


1263 13 


646 98 


^E39i 91 31 01 


563 85 


4964 6a 


45858 


641 69 


1253 07 


641 86 


K^33> 44 3> 55 


562 01 


5136 6a 


479 54 


663 So 


1340 73 


^35 09 ^ 
626 67 ■ 
616 6a " 


Kl2<>4 13 3> 94 


559 85 


5306 59 


499 92 


68567 


1225 09 


E3194 06 32 18 


557 41 


5474 14 


51968 


707 23 


1x06 15 


F 2121 32 32 26 


554 72 


5638 80 


53882 


738 43 


tiS3 92 


604 88 


■ 2046 00 32 iS 


551 8. 


5800 13 


557 29 


749 20 


1158 41 


59' 53 


1 1968 18 31 94 


S48 74 


5957 68 


575 «9 


769 49 


M39 68 


576 56 


' 18S7 96 3' SS 


545 52 


61 11 ot 


59* 18 


78935 


1097 76 


560 00 


1805 44 31 01 


542 20 


6259 70 


60856 


808 41 


1063 71 


541 88 


1720 73 30 31 


S3S »o 


6403 33 


624 19 


8i6 92 


1034 61 


522 23 M 


1633 93 29 47 


535 3S 


6541 48 


63907 


844 73 


9i*3 55 


501 11 ■ 


1545 11 2« 4I* 


53' 96 


6673 75 


653 16 


S61 78 


939 63 


478 55 ■ 


I4S4 43 27 36 


52857 


679978 


666 46 


87S 04 


892 93 


454 62 ^ 


1361 97 26 10 


525 M 


6919 18 


67895 


893 44 


&4361 


429 38 


1267 S6 24 71 


512 02 


7031 61 


690 61 


907 94 


791 78 


402 88 


1173 19 23 20 


5189a 


7136 73 


701 42 


921 50 


737 59 


375 2r 


1075 10 2t jS 


5' 5 97 


7334 24 


7" 39 


934 oS 


6S1 18 


346 44 ^ 


976 70 19 86 


S'3 21 


7323 8s 


72048 


945 65 


622 72 


316 64 H 


877 13 iS 04 


510 65 


7405 28 


728 70 


956 16 


56238 


285 90 H 


776 46 16 13 


50S 3» 


7478 30 


73604 


96s 58 


50033 


25432 ■ 


674 55 '4 '4 


506 23 


754268 


742 47 


973 89 


436 76 


221 97 ■ 


572 43 12 oS 


504 40 


7598 24 


748 CX) 


981 06 


371 85 


188 96 ■ 


469 30 9 97 


502 86 


7644 79 


752 62 


987 08 


305 81 


155 38 ■ 


365 61 7 So 


501 61 


7682 20 


756 3» 


99' 9' 


23883 


lai 34 ■ 


261 47 5 60 


500 66 


7710 36 


759 10 


995 34 


171 13 


86 94 H 


jt^ »57 01 3 37 


500 03 


7729 18 


76096 


997 97 


t02 8S 


VI. 1.1 ■ 


^^52 36 +1 13 - 


499 71 +77J8 60 


+ 761 88 


+ W» \«J 


- M \S 


~ M Mt B 



r 


r 

390 




Me^iri C'owell and Grommelin, 

Table I. — amtiHuat, 
SitoHd Qmidrant. IJtiil = oTmni. 


4 


r 


(4)' 


^ 


ji^ 3^, 


. (tf ^ 


^ 


1 '-' 


95 10 


367 so 


-6899 1779 


137' 20 09 59 65 


609 i 


■ '' 


86 23 


243 60 


60 60 1507 


>39 19 3' 57 39 


5 s; j 


1 '' 


78 4S 


"2 54 


53 42 ^182 


141 18 61 55 36 


5o« 4 


1 ^ 


7" 57 


203 77 


47 iti 1092 


>43 17 9* 53 45 


-.■M 


1 ^ 


65 53 


187 27 


41 80 933 


145 «7 36 SI 73 


H loi 


60 16 


173 48 


37 '4 800 


147 16 83 50 19 


385 ' 


103 


55 40 


159 32 


33 oS 687 


149 '6 34 48 77 


3S> > 


105 


51 .6 


147 58 


29 53 591 


151 15 90 47 4* 


3 *h^ 


107 


47 36 


156 96 


26 4t 509 


153 1$ 49 46 28 


^m 


109 


4398 


127 54 


23 69 440 


155 15 13 45 24 


^M 


in 


40 95 


119 05 


21 30 381 


1S7 14 80 44 2J* 


• sM 


113 


3S 33 


III 36 


19 17 330 


159 14 51 43 43 


308 1 


"5 


35 76 


104 4a 


17 29 aS6 


161 14 35 42 66 


mm 


J 119 


33 56 


y8 30 


15 64 249 


163 14 03 43 00 


'm 


3' 55 


92 49 


14 15 216 


165 13 Sa 4t 41 


^m 


121 


29 74 


87 34 


12 83 ISS 


167 13 64 40 8S 


X 30 


123 


»K 10 


82 67 


t 1 64 164 


i(J9 13 50 40 48 


1 01 


125 


36 6t 


?8 40 


>o 59 "43 


171 "3 37 4009 


o$i 


127 


35 36 


74 54 


9 63 125 


173 "3 a8 39 83 


6j 


139 


34 02 


7097 


8 77 109 


175 '3 21 39 6j 


4S 


131 


23 90 


67 75 


8 00 95 


177 '3 '6 39 48 


037 


'33 


31 88 


6i 53 


7 30 83 


179 13 »4 39 4a 


~ ** fl 


'35 


ao95 


62 15 


6 67 7a 




1 




When the distnrbiiijj force is due to a planet whose 
times that of tlie Sun, X and Y are tlie difterentiala of 


masa v^M 


1 






p 




J 



where p is tbo dUtanee between planet and oomet^ x\ j^, ^, 
)ieiiocentric cnunlinates iiiici distance of the planet. 



We may write 
or 



where 



v.= -^ 



V = V,4-V. 

V = V34-V, 

„ xz' + yy' + af 
v,j= -r 



Apr. 1907. The PerturhcUions of Halley's Comet. 391 

„ _ I I ra' + yy' + zz' 

Tbe advantage of the latter form ia that Yj can be dealt with 
in finite terms, whereas the disturbing forces arising from Y^ are 

of order — , where r is large. The form V = Vg + Y^ is therefore 

convenient for the parts of the orbit lying considerably beyond tbe 
disturbing planet. 

The integrals arising from Yj are 
m nj * ' \na dt J ^ a ^ \na dtj 'a 

m J ^ ^ \na dt J ^ a "^ Krvt dtJ "^^ a 

m J * ^\tui dtJ ^ a ^^ \7Ui dtJ '^' a 

dt is not iutegrable, but 

* * \na dt) * a * \na dt) * o 

It is convenient for brevity to call tbe leFt-hand side of this 
equation 

su that / dl^ is the perturbation of the mean anomaly at the next 
perihelion passage. 

The effect in arc of the elementary disturbance 'hi after an 

interval —-(is (zTr-nf)— . 
n n ^ 

In the above formulse 



392 



Messrs Coweii and Cr&mmelin, 






^' na i/t 




a^^-JL'l^ «' = _L(' 3X^-3,^1 






^^ ^^^JA^T.<^)\ 



2X 



Bat/( '^*'" a* 



fuin 



Arbitrary f.oiwtftntR may, of ooiirse, be added to the A**. E 
however, atiy constant be added Ui A| , vre Bhull have « Wn 
propurtumal to tbe tiiiiL iu A^. In A^ tlis constant +r nv 
introduced to create symmetry tiliout aphelion. It ia cjeorlr cab 
venioiit to introiliice the V = V3 + V^ method, and to drop it st 
pujots equidii^tnnt from aplielion. 

h is twice (lie urea conserved = na^^J{i — e'). 

Ill tliiH |>up«r ibe pertiirbiiliona by Jupiter between the r«tn7» 
of 1835 and 1910 are ctmsidereil. 

A prtliininary calculation liaving shown that the oomet vJT 
ruturij about 1910 ^iny, the tliBtuihing forces du<^ t-u Jupit«r u« 
calculated on the it-s-suniptioii that the coim't moves in us nn- 
diaturbed ellipao for which ^/{i -«*)>= '854000, and with a mi*ii 
motion Iws than Jupiter's iu the ratio 1 : srx '999151. 

The disturbing forces are calculated for every odd degree ot 
the comet's ec^M^ntric anomaly. Jupiter is supposed to move 10 an 
undiaturbed (.'Ui]>8c, and thit chaciges uf Jupiter'it mftun auomalt 
are 360" x '99915 1 times the chnnKeii of ni as given in Table L 

Jupiter's nieaa anuuiaty when u = o is usunicd tu have beci 

79'S^h .... M 

Jupiters eccentiicity in taken a^ 0*0482538. The ratio ^B 

mean motioaa implies a ratio ot mean distances 0*3939437. for 

(2jrx -999151)' (-2939437)3= I + ]^: ■ H 

7'he relative ponition of the two ellipses may be described ^^ 
follows : — 

The comet's iiaceniHng node on Jupiter's orbit is 46' 35' 
advance of Jupitur't) perilielion. The motion uf tlie com*t 
tetrograde auil its inclination U-> Jupiter's orbit ts tSo* •iS* 
The comet' It pt^rihidion is 113" 48' in the direction of ita 
motion from its node on AM\iufe'^* wtXAl. 



Apr. 1 907. 7%« Perturbations of Bailey's Comet. 393 

If f, Tf' be Jupiter's coordinates referred to its own axes, 

Ue- - ^ +( I - ^e'^) COB g' + { ~e' --e'^ jcoa 2/ + ^e'^ cos 3fif' + -e'* 00840* 
» 2\8/ \Z3/ 8 3 

L= ( I - |e'2 ) sin / + ( - e' - -^ e'* ) sin ag' + |e'' sin 3^ + - «'* sin 4/ 

f \8/ \2I2/ 8 1 



Expressions fur 



a'8f a'^'q' 



can be derived by a double differentiation. 
Besolviiig parallel to the comet's axes 



and 



— = + '1034 614 -^ - "2611 992 -^ 
a a a 



-^=-■2664 364 -^--iiSi 556 -5, 
a a a 



— = -0686 
a 



316 -^ + -0649 



3« -J 



0*3: 



^3-dM=+-i4zi 979 ---"ssSg 935 —J- 
r T^ r 

-A.iM=--366i 915 * --1623 937 —f 



'ti.i«= --0943 276 yJ-+-o892S32 ^^5 



V 

'8 



where rfM= 2° the interval betweeu succesaive values of « . 



Table II. gives these quantities with argument g' the mean 
anomaly of Jupiter. 

The table is etrictly appropriate to the revolution 1835-igio 
only J but small Hnear corrections would make it available for any 
other revolution : moreover, the small corrections need not be 
applied except when the distance between Jupitor and the cnrnet 
is small 



^H 394 


Messrs Cotoelt and Crt/mmriin^ 


"3 


^H 






Tablb : 


[1. 




M 


^^^^ 


Atffument' 


-JvpiUr'i 


1 Mean Anatnafi/. 


Unit O'Ooooj. 1 


^^^^^H 






c 
a 


as. 




^ 


^^^^^^H 


4 9S47 


-45358 


-«5 3» 


+ 156 98 


-404 as 


-10* IS 


^^^^^^H 


9367 


255 70 


64 13 


149 32 


407 62 


loz 21 


^^^^^^H 


8S 83 


257 73 


62 9(> 


141 60 


4to S3 


100 36 


^^^^H 


85 97 


359 ^7 


61 65 


• 3383 


413 86 


9836 


^^^^^B 


79 07 


361 51 


60 38 


136 ai 


416 73 


96 23 


^^^^B 


74 15 


363 37 


5909 


118 14 


4>9 43 


94 15 


^^^^1 


69 20 


264 93 


57 78 


no 22 


421 96 


92 04 


^^^^B 


64 23 


266 49 


56 45 


IC2 27 


4*4 3< 


89 ss 


^^^^H 


59 23 


267 97 


55 'o 


94 2S 


426 so 


s- 70 


^^^^H 


54 J' 


269 35 


53 73 


86 25 


42851 


«5 49 


^^^^^B 


49 17 


27063 


52 34 


78 » 


430 3-4 


S3 24 


^^^^^H 


44 l» 


271 82 


50 94 


70 13 


432 00 


8095 


^^^^^H 


39 05 


372 91 


49 5' 


62 04 


433 49 


7865 


^^^^H 


33 97 


273 91 


4807 


S3 93 


434 79 


7* 31 


^^^^1 


28 87 


374 81 


46 61 


45 Si 


435 93 


73 94 


^^^H 


23 76 


275 61 


45 14 


37 68 


43^ 89 


71 55 


^^^^1 


18 63 


376 32 


43 64 


29 56 


437 66 


69 13 


^^^H 


13 53 


37693 


42 14 


21 42 


43827 


66 69 


^^^H 


84' 


277 44 


40 62 


13 30 


438 70 


64 «3 


^^^H 


+ 3 28 


37786 


3908 


+ 5 19 


438 95 


61 74 


^^^^^B 


- I 85 


278 18 


37 53 


- 2 91 


43903 


59 S3 


^^^^^ 


b 98 


278 40 


35 97 


10 99 


43s* 93 


56 72 


^^H^ 


12 11 


37S 52 


34 39 


19 06 


43866 


54 17 


^^ 


17 a.l 


27855 


33 81 


27 09 


438 23 


51 61 


L M 


22 34 


37S 48 


31 21 


35 'o 


437 61 


49 04 


^^ 


27 45 


27831 


29 60 


43 08 


43'* 83 


4646 


^^L 


32 55 


278 04 


27 9S 


51 02 


435 86 


4386 


^^^^ 


37 ^ 


37768 


26 35 


5S92 


434 75 


41 25 


^^^^ 


42 71 


277 22 


24 71 


6(i 77 


433 46 


3S63 


^^r 


47 77 


276 67 


23 06 


74 59 


431 99 


36 01 


^^M 


53 83 


376 oa 


21 41 


82 34 


430 38 


33 39 


^H 


5784 


27528 


19 74 


90 04 


428 59 


30 74 


^^1 


6a 84 


274 44 


1808 


97 70 


426 65 


3S tl 


^V 


6753 


273 50 


t6 40 


105 38 


4»4 54 


25 45 


^^ 34 


72 79 


27248 


14 72 


tl2 So 


432 iS 


2Z 81 


■ 35 


77 72 


27 > 35 


13 03 


lao 26 


419 86 


ao 16 


I 36 


S3 6j 


270 14 


1' 34 


127 64 


417 29 


'7 52 


I 37 


87 5> 


268 83 


9 65 


134 95 


414 57 


14 88 


1 ^^ 


92 36 


267 43 


7 95 


142 19 


411 70 


12 23 


^^ 39 


97 >8 


265 94 


625 


149 34 


40S 70 


9 60 


^H 


101 96 


364 36 


4 54 


156 41 


405 54 


6 97 


^^H 


106 72 


362 69 


2 84 


'63 41 


40a 23 


4 34 


^^P 


■ II 43 


260 93 ' 


- t U 


170 31 


398 79 - 


I 74 


^^^ 


116 11 


359 08 ■ 


h 57 


177 12 


395 2a + 


87 


1 44 


lw>lA 


,»S1 I* 


11% 


\%^1U. 


VJi ^0 


3 47 


I 


- WS M 


-T^S \1 


^ -i^^ 


-\efi »f> 


-■?^ V^ 


'•^ v»^ 



Apr. igoy. 


The FerturbcUiuns of 


HalUy's 


Comet, 


395 ^H 






Tadlk 11.— emUwiuA/, 




■ 




i 




V' 










45 


- 125 34 


-255 13 + 3 9S 


- 190 46 


- 387 67 1 


05 ^^^1 


46 


12989 


253 01 


5 68 


197 00 


383 70 


63 ^^H 


■ 47 


"3441 


350 83 


7 39 


203 43 


37960 


It ^^H 


48 


13887 


348 54 


9 08 


209 75 


375 3« 


•3 72 ^^1 


49 


143 39 


246 18 


10 78 


315 98 


37' 04 


35 ^^^1 


50 


147 66 


343 74 


1247 


332 09 


366 58 


18 76 ^^H 


5' 


151 9S 


341 31 


14 16 


338 II 


362 01 


21 ^^^H 


5* 


156 z6 


238 61 


'585 


334 03 


357 33 


33 73 ^^1 


S3 


16048 


23 s **3 


'7 Sa 


239 81 


352 54 


19 ^^^H 


54 


164 64 


233 16 


19 20 


345 50 


347 64 


38 63 ^^H 


55 


16S75 


330 33 


30 S6 


351 07 


343 04 


3: 04 ^^H 


56 


172 81 


227 40 


33 53 


256 52 


337 54 


44 ^^H 


57 


17681 


224 42 


34 17 


261 86 


332 34 


35 81 ^^H 


58 


18075 


221 35 


3$ 83 


367 09 


3*7 OS 


■s ■ 


59 


18463 


21S 22 


*7 45 


273 19 


331 67 


40 ^^H 


60 


iSS 46 


215 Ot 


39 oS 


277 17 


316 30 


42 77 ^^H 


61 


192 22 


211 73 


30 70 


282 05 


310 6s 


04 ^^H 


62 


195 92 


308 38 


32 30 


38679 


305 01 


47 30 ^^H 


63 


199 55 


304 97 


33 90 


291 41 


299 30 


49 5' ^^H 


64 


203 12 


zoi 49 


3548 


»95 91 


293 51 


s> 70 ^^H 


65 


Z06 62 


'97 94 


37 06 


300 29 


387 65 


5386 ^™ 


66 


zio 06 


194 34 


38 62 


3<H 54 


281 71 


56 00 ^^^H 


67 


2"3 43 


190 66 


40 17 


308 67 


375 71 


10 ^^H 


68 


216 73 


t86 93 


41 71. 


312 67 


269 66 


60 18 ^^H 


69 


219 97 


183 14 


43 as 


316 55 


263 53 


62 21 ^^^H 


70 


223 »3 


179 39 


44 74 


3K> 3» 


957 35 


64 23 ^^1 


71 


2x6 22 


•75 3« 


46 24 


323 94 


251 II 


32 ^^H 


7» 


229 24 


171 42 


47 73 


327 45 


24462 


68 16 ^^H 


73 


332 19 


167 40 


49 18 


33083 


338 49 


7009 I^H 


74 


235 06 


163 33 


5063 


334 08 


232 10 


71 97 H 


75 


337 S6 


159 20 


32 07 


337 20 


225 68 


7381 ■ 


76 


240 59 


•55 03 


53 49 


340 21 


219 30 


73 64 ■ 


77 


343 34 


150 81 


54 89 


343 09 


213 70 


42 ■ 


78 


345 81 


146 54 


56 27 


345 84 


306 16 


79 >8 ■ 


79 


24831 


•42 33 


57 64 


34846 


199 59 


So 89 ^^H 


So 


250 73 


13787 


5899 


35097 


192 98 


8357 ^H 


8i 


25307 


133 47 


60 32 


353 34 


18635 


33 ^^H 


S3 


"55 33 


13903 


61 63 


35560 


179 69 


85 83 ^H 


83 


aS7 52 


134 55 


63 93 


357 74 


173 o> 


4i ^^H 


84 


259 62 


120 03 


64 19 


359 75 


166 31 


S895 ^H 


85 


261 65 


"5 47 


65 45 


361 63 


159 59 


90 ^^H 


86 


263 6d 


tio 88 


66 68 


363 40 


'5285 


9> 93 ^^1 


87 


265 46 


106 25 


67 89 


36504 


146 II 


93 37 ^^H 


8S 


267 24 


101 60 


69 08 


36657 


•39 36 


94 ^^H 


89 


268 95 


9691 


70 26 


36798 


»ii S9 


^^ ^^1 


90 


- 370 j; 


- 93 19+71 41 


-369 37 


- \^S %\ 


^ 41 ^^H 



^M 396 


Messrs Cowell and (Jrommelin^ 


3 


^^^ 




Tabli W.—tmiinutd. 




<1 


^^^^t 


Argununt — Jnpilvr's 


r il/ttin ^nomafy. Unit otxiooi. | 


^^^^^^^H 


g 


g_ 


^ 


■"^^ 


■V^ 


^*. 


^^^^H 


a 


» 


a 


"TS-**" 


-prA« 


TT*" 


^^^^^^^^^^1 
^^^^H 


- 270 S7 - 


92 19 +71 41 


- 56^ 37 


- tas 81 


-^97 45 


^^^^H 


272 II 


87 44 


72 54 


370 44 


119 04 


98 74 


^^^^H 


*73 56 


82 67 


73 64 


37' 50 


iia a6 


100 00 


^^^^1 


374 94 


77 87 


74 73 


372 42 


105 4S 


101 33 


^^^^1 


27623 


73 OS 


75 79 


373 26 


9« 71 


103 41 


^^^^1 


»77 44 


68 20 


7683 


373 96 


9> 93 


'03 55 


^^^1 


378 57 


63 34 


77 ^ 


374 55 


85 »7 


IU4 66 


^^^^1 


279 61 


58 46 


78 84 


37503 


7« 43 


10$ 7* 


^^^H 


280 jS 


53 56 


798. 


375 41 


71 67 


106 77 


^^^^1 


2S1 45 


4864 


8075 


37566 


64 94 


If? 79 


^^^^^H 


282 3S 


43 71 


81 67 


375 8' 


58 32 


io« 75 


^^^^^H lot 


2S2 96 


3877 


82 57 


375 S5 


5' 5* 


109 68 


^^^^^^^H 


283 59 


33 to 


83 45 


375 79 


44 83 


110 57 


^^^H 103 


284 13 


3885 


84 30 


375 62 


38 »7 


Jll 44 


^^^^H 


a84 59 


23 SS 


85 12 


375 34 


31 S* 


113 36 


^^^^^1 


284 97 


tS 90 


8s 92 


37496 


24 SS 


"3 05 


^^^^H 


28s 26 


13 9> 


86 69 


37448 


18 38 


113 So 


^^^^^^H l<>7 


28s 48 


8 92 


87 44 


37390 


II 70 


114 S* 


^^^H 


28; 61 - 


3 93 


88 17 


373 2' - 


5 16 


11$ 31 


^^^^H 


285 65 -t 


1 06 


8h 86 


372 4' + I J6 


115*5 


^^^^^^H tio 


2»5 62 


6 05 


89 54 


37" S3 


78s 


116 46 


^^^^^^ til 


28s 50 


II 04 


90 iS 


370 55 


'4 31 


117 05 


^^^B 112 


285 30 


1603 


90 81 


369 47 


20 74 


"7 59 


^^1 "3 


2S5 02 


31 03 


9' 4P 


368 29 


27 14 


118 11 


^^H l>4 


38465 


25 99 


91 97 


367 03 


ii 49 


118 59 


^^m "^ 


2S4 30 


30 96 


92 51 


3<»5 67 


3981 


119 oj 


^^^1 


2S368 


35 93 


93 03 


364 21 


46 10 


«I9 44 


^^M 117 


383 07 


4088 


93 52 


362 67 


52 35 


119 83 


^^H ti8 


982 38 


45 8> 


93 98 


361 03 


58 SS 


I30 15 


^^M 119 


3S1 63 


5074 


94 42 


359 3> 


64 72 


lao 46 


^^^1 


28077 


55 65 


9483 


357 50 


70 84 


i20 7j 


^^H I2t 


279 84 


6055 


95 31 


35360 


76 9K 


lao 98 


^^^1 132 


27S84 


65 43 


95 5« 


353 ^i 


82 95 


131 19 


^^1 >23 


277 76 


70 39 


95 90 


35' 56 


88 94 


131 J7 


^^H 


2;6 59 


75 '3 


96 20 


349 4 1 


94 89 


tsi 53 


^^H I3S 


375 35 


79 95 


96 47 


347 18 


100 7S 


■ 31 63 


^^1 


274 04 


8475 


96 72 


344 87 


to6 64 


121 72 


^^1 137 


272 64 


i9 52 


96 94 


342 48 


"12 43 


121 77 


^^M 


271 IS 


94 27 


97 14 


340 02 


liS 18 


131 79 


^^H 129 


269 6j 


9S 99 


97 30 


337 47 


123 88 


131 78 


^^m '3° 


268 02 


loj 69 


97 44 


33486 


'29 S3 


131 75 


^^M *v 


266 32 


loS 36 


97 56 


332 t6 


■35 n 


131 «8 


^^M ijz 


264 


112 99 


97 64 


329 39 


140 67 


131 58 


^^M 133 


z6z 72 


117 60 


97 7' 


326 55 


146 t6 


tai 42 


^^L^ 


260 So 


\n v\ 


«n ^\ 


^n^i 


>S> 60 


131 aS 


^^^^^ 13S- 


-as8 %% 


■y\-A 1\ 


^■¥1 1^ 


-■^in bij 


^■^*i» '=?b 


'■■^XSO^^ 



&pr. 190; 


. 7%tf Perturbations of ffalley'B 


Oonj^U 


397 ^I 






Tablb l\.—mniinw*L 




■ 




Aryument — Jupiter's Mean Afumtat;/, 


O'OOOOI, ^^^1 




a* 


^_ 


r 


oV 


aV 


•v^ ^^^B 


¥ 


• 


'a 


flT 


-prd« 


7T<'«« 


7?^ ^H 


'35 


-258 82 


+ 126 71 


+ 97 74 


-J20 65 


+ 156 98 


(-121 09 ^^H 


'36 


256 77 


131 32 


97 72 


317 60 


162 30 


12088 ^^1 


137 


254 64 


13568 


9768 


314 48 


167 S6 


ISO 6s ^^^1 


138 


252 44 


140 IZ 


97 60 


311 29 


172 77 


^^1 


»39 


250 18 


144 SI 


97 50 


30803 


177 92 


130 04 ^^^1 


140 


247 85 


148 86 


97 37 


304 72 


183 01 


119 71 ^^H 


141 


MS 45 


153 >8 


97 32 


30' 33 


188 04 


^^1 


14s 


24* 99 


'57 45 


97 04 


297 88 


»93 02 


118 96 ^^1 


'43- 


240 45 


i6t 68 


9683 


294 37 


197 94 


54 ^H 


144 


237 86 


165 86 


96 6a 


290 So 


20Z 79 


09 ^^H 


MS 


=35 »> 


170 00 


96 34 


287 17 


207 58 


117 62 ^^^1 


146 


232 47 


174 10 


96 05 


283 48 


312 30 


13 ^^H 


U7 


22968 


178 14 


95 74. 


279 74 


216 97 


116 6t ^^H 


148 


226 83 


182 14 


95 40 


275 93 


221 58 


06 ^^^1 


M9 


223 92 


186 09 


95 04 


272 06 


226 12 


115 4S ^H 


ISO 


22095 


189 99 


94 65 


268 15 


230 60 


1:4 87 ^H 


>5' 


217 92 


193 84 


94 24 


264 19 


235 01 


114 25 ^^H 


151 


21483 


197 64 


93 80 


260 16 


239 36 


'^3 59 ^^1 


>53 


211 68 


201 38 


95 33 


256 09 


243 64 


113 91 ^^^H 


•S4 


20S4S 


»S 07 


9284 


2SI 96 


Z47 86 


113 21 ^^^1 


155 


205 23 


20S 71 


92 33 


247 78 


252 DO 


tit 47 ^^H 


156 


201 90 


2tZ 28 


91 79 


243 56 


256 09 


110 72 ^^^H 


'57 


198 53 


215 81 


91 22 


239 27 


260 11 


109 ^^1 


'58 


195 H 


219 27 


90 64 


23495 


264 06 


109 14 ^^H 


159 


191 64 


222 68 


90 02 


230 58 


267 94 


32 ^^H 


160 


188 II 


226 02 


8939 


226 16 


271 76 


107 47 ^^1 


i6t 


184 54 


2*9 3' 


8873 


221 71 


275 51 


106 60 ^^H 


l6z 


iSo 91 


23* 54 


88 04 


217 20 


279 18 


105 70 ^^1 


i6j 


"77 24 


235 70 


8733 


212 64 


28280 


104 79 ^^1 


164 


173 52 


238 80 


86 60 


20S 05 


28633 


10584 ^H 


165 


169 75 


241 84 


8585 


203 41 


289 80 


I03 ^^H 


166 


165 94 


244 81 


85 08 


198 74 


393 30 


101 89 ^^H 


1 167 


162 09 


247 72 


84 28 


194 02 


296 S3 


too ^^1 


^H]68 


■58 19 


25056 


8346 


189 26 


299 79 


998s ^H 


H 169 


154 »5 


253 34 


8261 


184 47 


302 98 


98 ^^H 


170 


150 37 


256 04 


81 75 


179 63 


306 10 


97 72 ^^1 


171 


146 as 


258 68 


80 86 


'74 77 


309 14 


9663 ^H 


17a 


142 19 


261 26 


79 95 


169 86 


312 12 


95 51 ^^1 


173 


138 09 


363 76 


79 02 


164 92 


315 0' 


94 ^^1 


174 


'3396 


366 19 


7807 


'59 95 


317 &4 


93 21 ^^1 


175 


129 79 


268 56 


77 10 


'54 93 


320 59 


92 04 ^^1 


176 


125 59 


2708s 


76 u 


149 89 


323 27 


9084 ^H 


177 


121 35 


273 07 


75 10 


144 81 


32588 


89 61 ^^H 


.78 


117 08 


275 " 


74 06 


139 7' 


328 40 


88 38 ^H 


179 


112 78 


277 29 


7301 


134 57 


^yisi 


%i v-k ^^H 


180 


-10B4J +379 39 +71 94 


-119 i,\ +513 4S 


\ %^ %%, ^H 


^_ 


^H 









^ 


^^ J 



^m 


Msssra CmoeU ai\d Crommeliti, 


UjJ 


^^^^ 




TasLI \t—ro7Ui»umt. 




fl 


^^^^b 




1 3Imn A 


namaljf. 


Unit o-Qoooi. B 


^^^^^^^H 


«* 


t/i 


t_ 


"^'j 


■V. aar ^^H 


^^^^^1 


a 


tt 


A 


•^dit 


-^^« 


?*^^^H 


^^H 


-108 45 +279 29 


*7' 94 


- 139 41 


+ 333 35 + 


8s «4 


^^^^H iKi 


104 10 


281 32 


7085 


124 21 


335 55 


84 V4 


^^^H 183 


99 71 


38307 


69 74 


n8 99 


337 78 


83 33 


^^^1 183 


95 29 


28485 


6S 63 


"3 73 


339 94 


&I S9 


^^^H 


90 86 


2H6 56 


67 47 


108 45 


343 01 


8054 


^^^H iss 


86 40 


388 18 


6631 


103 15 


344 01 


79 16 


^^^^H 


Si 93 


3S974 


65 13 


97 81 


345 94 


77 77 


^^^H t87 


77 41 


291 31 


63 93 


92 46 


347 79 


7636 


^^^^P 


73 88 


393 6t 


62 73 


87 08 


349 56 


74 93 


^^^^^F 


6834 


293 93 


61 49 


81 67 


351 26 


73 49 


^^^^L 


637s 


395 »7 


6a 34 


76 25 


352 86 


73 03 


^^^^B 19] 


59 » 


396 34 


58 98 


70 81 


354 40 


70 54 


^^^^^^B 193 


54 60 


297 42 


57 70 


65 34 


355 85 


69 <q 


^^^^H 193 


49 99 


29S 43 


56 41 


5984 


3S7 =3 


67 53 


^^^^H 


45 37 


39935 


55 '0 


54 34 


3S8 53 


65 99 


^^^H 195 


40 73 


300 20 


53 77 


48 81 


3S9 74 


^ 44 


^^H 


3608 


30097 


53 44 


43 37 


360 87 


62 ss 


^^^^H 


31 43 


301 66 


51 08 


37 7a 


361 9* 


61 39 


^^^^H 


36 76 


302 37 


49 73 


33 '4 


362 90 


59 70 


^^^H 


33 09 


302 79 


4834 


» 53 


363 79 


5808 


^^^^^H 


17 4" 


303 34 


46 95 


20 94 


364 60 


56 45 


^^^^^^r 


13 73 


303 61 


45 54 


>5 3* 


365 3a 


54 So 


^ 


S 04 


303 89 


44 13 


9 69 


36s 96 


53 M 


^^M 


- 3 35 


304 10 


43 70 


- 4 OS 


366 SI 


51 47 


^^m 


+ ' 33 


304 33 


41 26 


+ I 60 


366 99 


49 78 


^^^1 


6 03 


304 26 


3981 


7 36 


367 38 


48 07 


^^H 


10 71 


304 22 


38 35 


12 94 


367 68 


46 35 


^^^B 


'5 39 


304 10 


36 88 


iS 61 


367 90 


44 61 


^^■^ 3d8 


SO 07 


303 90 


35 40 


24 30 


368 04 


43 87 1 


^^^^^K 


34 75 


30361 


33 90 


29 99 


3^ 09 


41 >i ■ 


^^^^^^f 


39 4« 


303 35 


32 40 


35 69 


368 04 


39 33! 
37 S4| 
35 74^ 
33 93 
3» 09 
30 a6 


^^^^^^ 311 


3408 


303 80 


30 90 


41 38 


367 93 


^^^H 312 


3873 


302 27 


39 38 


47 " 


367 70 


^^m 3u 


43 37 


301 66 


37 85 


53 83 


367 41 


^^H 314 


47 99 


30097 


»6 32 


5852 


367 02 


^H SIS 


53 61 


300 ao 


34 78 


6433 


366 54 


^^^1 


57 31 


399 34 


33 34 


6994 


365 97 


28 4t 

3*54 

34 68 


^H 317 


61 80 


398 40 


21 68 


756s 


365 3a 


^^1 3lS 


6637 


397 39 


20 12 


81 36 


364 58 


^^H 319 


7092 


296 29 


18 56 


87 07 


363 74 


33 79 
30 89 

IS 9* 

>S 14 ■ 
t3 «afl 

v\ ^ ■ 


^^H 


75 45 


295 11 


16 99 


92 76 


36i Si 


^^^1 331 


7996 


2938s 


IS 42 


9845 


361 80 


^^^H 233 


84 45 


292 SI 


1384 


104 13 


360 69 


^H 323 


88 93 


391 10 


12 26 


109 82 


3S9 50 


^^1 


93 1^ 


3&9 60 


to 68 


115 48 


358 30 


^^^. 325 


+ 97 7* +^* ox + q wj 


^\*v VT,Vv^%,^^ 



Apr. 1907. The JPertu-rbationa of HtUley'$ Comtt. 


399 ^I 






Tablk ll.—roHti»ktd. 




m 




^rgtuntnt^-JupiUr't .Vinu Ancntalit, 


[Jiiito'ooooi. ^^^1 




r 


y" r 


oKi- . 


a!»ii- 


a^r ^^^1 


r 


a 


a • 


^<l« 


T'^" 


^H 


225 


+ 97 78 + 288 01+ 909 


+ 131 13 


+ 356 82 


t- 1> 25 ^H 


326 


I03 16 


286 36 7 so 


126 78 


355 34 


^^1 


227 


106 53 


284 63 5 90 


132 4T 


353 78 


^H 


22S 


110 S6 


382 81 4 31 


I3S 03 


352 11 


^H 


a29 


115 16 


280 92 2 72 


143 64 


350 35 


33S ^M 


230 


119 43 


278 95 + 1 13 


149 23 


34S 51 + I 39 ^^1 


231 


123 69 


276 90 - 48 


"54 79 


346 56- 


■ ^^^H 


232 


127 87 


374 78 2 07 


tbo 34 


344 52 


2 61 ^^M 


233 


132 04 


272 s« 3 67 


165 86 


342 39 


4 61 ^^^1 


»34 


136 16 


270 30 5 2fi 


171 37 


340 16 


6 63 ^^M 


2J5 


140 26 


267 95 6 86 


176 86 


337 84 


8«5 ^^1 


236 


144 31 


265 53 8 45 


182 31 


335 4« 


10 ^^M 


*37 


14833 


263 03 10 04 


187 74 


332 90 


13 71 ^^M 


^3S 


152 29 


260 45 II 62 


■93 '5 


330 29 


14 75 ^^1 


^39 


156 22 


257 80 13 20 


198 53 


32758 


16 78 ^^1 


240 


160 10 


25s oS 14 78 


303 88 


324 78 


■883 ^H 


241 


163 94 


252 29 16 36 


309 19 


311 88 


20 ^^H 


242 


167 74 


249 43 17 9J 


214 47 


318 89 


22 93 ^^1 


■'43 


171 48 


246 50 19 49 


219 71 


3' 5 79 


^H 


244 


175 18 


243 49 31 05 


224 93 


312 60 


27 04 ^^M 


»45 


178 S2 


240 42 22 61 


230 09 


309 3» 


29 09 ^^M 


246 


IS2 42 


237 28 24 15 


23s 23 


305 9i 


31 IS ^H 


247 


IS596 


»34 07 25 69 


240 31 


3<*2 44 


33 2> ^H 


248 


18945 


23D 79 27 23 


245 37 


298 86 


35 27 ^^1 


249 


19a 89 


337 45 as 75 


250 37 


295 "9 


37 33 ^^M 


250 


196 27 


224 04 30 27 


3SS 33 


391 41 


39 38 ^H 


251 


199 59 


220 $6 3' 78 


260 23 


387 54 


41 43 ^H 


252 


202 S6 


217 03 33 28 


265 09 


28358 


43 49 ^^1 


»53 


306 06 


»'3 43 34 77 


269 90 


279 52 


54 ^H 


854 


209 21 


309 77 36 34 


274 66 


*75 36 


47 ^H 


»$5 


313 jO 


306 04 37 7 1 


279 36 


271 to 


49 ^3 ^^1 


256 


215 32 


302 26 39 17 


384 00 


266 75 


Sr 66 ^^1 


aS7 


2tK 28 


1 98 42 40 6] 


288 58 


362 29 


53 70 ^^M 


258 


321 18 


194 52 43 05 


393 'I 


257 76 


55 73 ^^M 


^ 259 


224 02 


lOu 56 43 47 


297 57 


253 '2 


74 ^^1 


^H a6o 


226 78 


186 55 44 88 


301 97 


248 38 


59 77 ^^1 


H a£i 


329 48 


182 48 46 28 


306 30 


343 56 


6t 77 ^^M 


262 


332 II 


17S 36 47 66 


3>o 57 


23863 


63 77 ^^1 


263 


334 68 


174 iS 49 03 


3'4 77 


333 62 


6576 ^H 


364 


337 17 


169 96 50 38 


31889 


228 SI 


67 74 ^^1 


265 


»39 59 


165 68 51 72 


322 94 


223 3» 


6971 ^H 


266 


241 94 


161 35 53 04 


326 93 


218 01 


71 67 ^^^H 


267 


244 22 


'56 98 54 35 


33083 


212 64 


73 6z ^^^H 


368 


246 43 


15a 56 55 64 


334 64 


207 [6 


75 ^^^H 


269 


24856 


148 09 56 91 


33838 


2QI 60 


11 ^^1 


270 


+ 330 6i +143 57 -58 17 




■vi'JSSS 


- n^) v> ^^M 



^^ 400 


Messrs C'otoeil and Cromm 


elin. 


Lxvnf^ 


^^^ 




Taiilb ll.—eonttniud. 




u 


^^^B 


Arifumtnt — JupUer't 


Mtan Anomaly. UDitO'OOOOi. J 


^^^^^^^H 


x' 


V 


«■ 


**^j. 


«v. 


«>^._^H 


^^^^^H 


a 


a 


a 


r^*" 


^r*» 


^^^ 


^^^^^^g 27a 


+ 250 61 + 143 57 


-58 17 


+ 342 03 4^ 195 95 


- 79 39 


^^^H 271 


252 60 


139 02 


59 41 


345 60 


190 ai 


81 39 


^^^H 373 


254 SO 


134 43 


60 63 


34909 


184 38 


83 16 


^^^H 


256 32 


129 78 


61 S3 


35348 


(78 47 


8503 


^^^^1 


25S 07 


125 10 


63 03 


355 78 


17* 47 


8687 


^^^H 27s 


359 74 


120 38 


64 18 


35899 


166 39 


88 70 


^^^m 


261 33 


115 63 


65 33 


363 it 


i6o 33 


90 51 


^^^^f 


262 tS4 


110 84 


6645 


365 '3 


.»53 99 


93 it 


^^^K 


264 27 


106 02 


67 56 


36804 


147 65 


94 09 


^^^^B 


265 62 


loi 16 


68 64 


37086 


141 35 


95 &4 


^^^^H 


266 88 


96 37 


69 70 


373 57 


134 7« 


97 57 


^^^^1 


26S 06 


91 35 


7074 


376 18 


128 31 


99 «7 


^^^^H 


269 16 


86 41 


71 76 


37868 


131 58 


100 96 


^^^B 


270 18 


8i 43 


73 76 


381 07 


114 8S 


103 62 


^^^B 


271 II 


76 44 


73 73 


383 35 


108 10 


104 36 


^^^H 


271 95 


71 4' 


7468 


385 S3 


101 36 


IDS 87 


^^^H 


272 71 


6637 


75 61 


387 53 


94 34 


«07 45 


^^^H 


373 39 


61 30 


76 5» 


38951 


87 37 


109 01 


^^^^1 


373 97 


S6 22 


77 39 


391 33 


80 ja 


110 54 


^^^^V 


274 48 


51 13 


7835 


39303 


73 21 


113 04 


^ 


274 89 


46 00 


79 08 


394 60 


66 OS 


113 5< 


^^m 391 


275 22 


40 86 


7988 


39605 


58 «3 


"4 95 


^^H >92 


275 45 


35 73 


8066 


397 37 


51 54 


ir6 36 


^^1 393 


375 60 


30 56 


81 41 


39857 


44 31 


117 74 


^^H 


275 67 


35 39 


82 14 


39964 


3683 


119 oS 


^H 395 


375 64 


20 21 


82 84 


40057 


»9 39 


I30 3^m 


^^^1 


375 5« 


1503 


8353 


401 37 


31 91 


^^1 297 


275 32 


984 


84 16 


403 05 


14 40 


123 89 


^^H 


375 03 + 4 65 


8478 


403 57 + 6 83 


134 10 


^^1 


274 64 - 


54 


8538 


402 97 - 


77 


135 36 


^H 


374 >7 


S 73 


85 94 


40333 


84a 


136 39 


^^H 301 


373 61 


10 93 


86 48 


403 35 


16 09 


137 48 


^^H 


272 96 


16 11 


86 98 


403 33 


^3 79 


»3S 53 


^H 303 


272 22 


21 39 


87 46 


403 i6 


3< 5a 


139 S3 


^^M 3°4 


371 39 


26 47 


87 93 


40s 84 


39 36 


130 50 


^H 305 


270 47 


3' 63 


8834 


403 39 


47 04 


131 43 


^H 306 


269 47 


36 79 


8873 


401 78 


54 84 


133 30 


^H 3^7 


26837 


41 93 


89 10 


401 03 


62 64 


»33 13 
133 93 


^H 30S 


267 18 


47 06 


8943 


400 14 


70 46 


^H 3^ 


265 91 


53 17 


8973 


39909 


78 29 


13468 

»35 3& 
13603 
136 64 
»37 30 


^^H 31<> 


264 55 


57 37 


90 Dl 


397 89 


86 12 


^H ^" 


263 10 


63 35 


90 26 


396 54 


93 96 


^H 312 


261 56 


67 40 


90 47 


395 05 


»oi 80 


^^L^ 313 


35993 


73 44 


9065 


393 40 


»09 63 


^^^B 314 


2S& 12 


71 ^i 


gQ%\ 


Viv«o 


^*1 46 


^^■^ 3»S 


+ 35* 43 


- »2 *i 


-SO^^ 


^■i?*4fe<V 





Apr. 1907. Tiie Perturbatums of Halley'i 


Comet. 


401 1 






Table 11. — eomliniud. 




^M 




ArpuntwX' 


-JupUa*! Mtan Anomaiy. Unit 0*0000 


^^^H 




# 


»• 


/ 


aMr- 


oV . ■> V - ^^^1 


if 


5 


■ 


• 


i^d- 


—du - 


^^m 


3»5 


+256 4a 


- 8343 


-90 93 


+ 38964 


- 135 25 - 


■7 ^H 


316 


254 53 


8738 


91 D2 


3S7 52 


'33 04 


59 ^^^M 


317 


353 56 


93 31 


91 09 


385^6 


140 Sa 


95 ^^^H 


318 


»50 50 


97 31 


91 12 


3S385 


14857 


39 ^^^^1 


319 


24836 


102 07 


91 tz 


380 29 


156 39 


39 53 ^^H 


3*3 


246 13 


106 90 


91 09 


377 57 


16398 


73 ^^1 


331 


143 8a 


111 69 


91 03 


374 70 


171 64 


39 ^^M 


3za 


241 43 


116 44 


9093 


371 67 


179 26 


99 ^^H 


323 


a3S9S 


lai IS 


90 8i 


36S49 


1S6 S3 


^^H 


3»4 


336 39 


•3583 


90 66 


365 16 


"94 37 


04 ^^H 


325 


333 75 


130 46 


90 47 


361 68 


201 86 


^^M 


326 


231 03 


13504 


90 as 


358 at 


209 aS 


39 87 ^^M 


327 


238 23 


'39 58 


90 01 


354 36 


3l6 66 


71 ^^H 


32S 


235 36 


"44 07 


8973 


350 34 


223 97 


39 49 ^^M 


339 


222 40 


148 5' 


89 42 


346 26 


23" =3 


39 22 ^^H 


330 


319 37 


153 90 


89 08 


343 04 


33S 40 


89 ^^M 


331 


316 a6 


157 33 


88 71 


337 67 


345 5" 


3^5" ^H 


332 


JI3 08 


161 51 


88 30 


333 15 


352 54 


07 ^^M 


333 


ao9 83 


165 74 


87 87 


328 50 


359 49 


37 57 ^^1 


334 


206 50 


169 tJQ 


8741 


333 70 


a66 36 


02 ^^M 


335 


203 to 


174 02 


86 9a 


318 76 


373 M 


^^H 


336 


199 63 


178 06 


8639 


3' 3 70 


27983 


35 ^^1 


337 


196 09 


tSa 05 


8584 


308 49 


386 43 


3505 ^^M 


338 


193 48 


1 85 98 


85 a6 


303 u 


39393 


34 37 ^^M 


339 


1S8 80 


189 83 


8464 


397 67 


299 3'. 


33 ^^M 


340 


18s 06 


193 63 


84 00 


292 07 


30s 59 


33 57 ^^1 


341 


iSl 25 


'97 35 


S3 33 


3S633 


311 77 


31 64 ^^M 


342 


17738 


201 00 


82 63 


280 48 


31784 


3" ^^M 


343 


'73 45 


ao4 59 


81 90 


274 5" 


3^3 79 


39 61 ^^^H 


344 


169 46 


208 10 


Si 14 


36S 40 


329 62 


SI ^^M 


345 


165 40 


211 54 


8035 


262 18 


335 33 


^^M 


346 


l6t 39 


31491 


79 54 


355 85 


340 91 


^^^M 


347 


157 13 


21S 20 


7869 


249 41 


346 37 


24 91 ^^H 


348 


isa 90 


Z2I 41 


77 82 


243 86 


35' 69 


33 61 ^^^H 


349 


148 63 


224 54 


76 92 


236 21 


356 88 


22 ^^^H 


350 


144 30 


227 60 


76 00 


229 44 


361 92 


20 84 ^^^H 


35» 


139 93 


230 58 


75 04 


222 59 


366 S3 


19 39 ^^M 


3SZ 


'35 49 


233 47 


74 06 


215 64 


37' 60 


"7 ^^H 


3S3 


131 01 


236 28 


73 06 


208 59 


376 ar 


32 ^^^H 


354 


12649 


23901 


73 03 


aoi 46 


380 68 


14 72 ^^M 


355 


121 92 


241 66 


70 97 


194 24 


38501 


■3 07 ^^H 


356 


117 3> 


244 21 


6989 


18693 


389 17 


11 37 ^^M 


357 


112 66 


246 69 


68 78 


"79 55 


393 iS 


09 6a ^^^1 


358 


107 96 


249 07 


67 65 


172 10 


397 03 


0^ &a, ^^^1 


359 


103 24 


251 37 


66 50 


164 s* 


Apo ^X 


\<:fe c>\ ^^^1 


36Q 


+ 9S47- 


^53 58 


-6s 32 


+ IS6 ^ 


-tfii,Vi 


- ^^K ^"^ ^^M 


^^^H 


^^m 


^^ 


^^ 




^m 


^^^^^H 



w 


403 JIAwrs CVuW/ and Crommelin. LXVIL 6, ^i 


H 


TaMe III. DOW gives, for argumeot n, the vulues of >j' JufHter'i ^4 


^H 


meftn anoDitly and a-'S.'ht, d'\tiu^ a^Z/lu for Ui« fint uiid fourth 1 


^H 


quadnuiU ; and a'-'X^'/u, d'Y^lu, a-Z^du for the second «nd thiiU ^^ 


^1 


quadrautfl. ^^| 


^H 


The V=Vj + V^ melbod is uwd for the aocond and lliird ^i 


^1 


qitadratito. The discontinutW in the numtricul values ao X, V, Z 


^H 


are rephicwi by X^, Y^, Z,, illustrate the value of the method. 


^H 


The %alue« of /, are nut required id this paper, hut will h« , 


^H 


made uae of when we compute the change of the pluoe of the orbit. ^H 


^^^^ 


We have ^M 


^B 


-V- /a* ""x / - "*'* *' fl'^y v' ^H 


^M 


— , /a* a'\ , . a*xu z' o*u^ v' ^H 


^r 


The romputatjon requires the valuee of -V ^-zj-' —15- »m ^H 


■ 


*-;- for the lecond (and third) qnadrauta. These functiona have ^H 


^H 


therefon* Iwen included in Table I. ^H 


^1 


The third and fourth quadrantii are written oat in the rerurve ^H 


^1 


orJi^r, so as to prrserve the onler uf the auxiliary qoantibiea given ^H 


^^^ 


in Table 1. ^H 


^^M 


^^ Table ^M 


^^1 


^H yirtt ^tuKlnHiA Uoit o-oooi. ^| 


^V^^ 


^^r* ^XAi ^v*t #u« 


«a*i i^Tfc ^^^1 


^H I 


■ 
79'53» +5 5**- 457 - 2 10 


47" 119^51 39 43! its 57 ^^1 


1 ^ 


79^S3 6 54 401 a a» 


49 134'379 68 44 119 74 'O^M 


■ 5 


8o*395 7 34 333 a 4i 


ji 139*130 99 10 105 91 te^H 


H ^ 


80-874 8 oa 3 S4 '50 


53 134*209 115 15 78 26 65^H 


H 9 


81*406 8 59 1 60 2 54 


55 I39'636 110 61 SI 70 ^1^1 


1 " 


Sa-ooj 9 05 -f 5J c 52 


57 US'392 94 21 35 36 n^M 


B '^ 


82-679 9 43 - 71 a 47 


59 I5'"5'4 75 93 »* 34 8 JF" 


■ 15 


83453 9 71 3 14 2 i$ 


6i 157^99 60 18 26 78 + 66 


H *' 


•4*334 9 9' 3 79 a i» 


63 164-853 47 43 »7 74 - 3 S3 


H '^ 


Sj'^t 10 01 $68 19} 


65 I72«8$ 37 07 »9 68 S $5 


^H " 


86*485 10 03 7 86 1 S7 


67 179703 38 35 31 78 6 3tf 


■ '^ 


87783 9 93 '0 39 ' '• 


69 187707 ao 65 33 69 6 8iJ 


m *^ 


89*144 9 74 <3 3' - 48 


71 196-113 13 s* 35 17 smM 


~ a? 


90'SS8 9 40 16 71 *- 36 


73 204-914 6 73 36 06 aJH 


]_ •* 


92*793 8 93 20 71 148 


75 214123 + 36 >6 ^^H 


k^' 


94758 » 3» a$ 43 » 99 


77 "374t - 6 4t 35 60 - I jH 


P» 


97X117 7 59 3' '1 5 03 


79 333773 "82 33 97 ■»■ fc 


^ 3$ 


99*jo6 6 80 J7 97 7 85 


8t 344*218 19 03 31 22 a 67 ' 


37 


109^36 6 ij 46 33 M 76 


83 255 T*4 14 87 17 21 4 i^ 


39 


los-aaj 5 94 56 66 17 27 


85 266-372 30 11 «i 83 i^M 


41 


108477 7 OS 69 ja 25 oj 


87 378t>8o 34 39 1$ oa ^H 


43 


ll2'an9 11 01 Bo 31 3S 85 


89 29o-ai3 . 37 a? - 6 Sj 4-I^H 


i: 


llj-829 30 6« 03 17 50 23 


' 



Apr. 1907. 


The Pertwhaiums of HalUj/s Comet. 




403 ■ 








T^BLB Ul.—fxmtinntd, 






1 


ttemd QvMdraiU, 


Jnitotwoi. 




Third i^adrraU. tJiiit o-ooot. H 


•y 


a- 


S.^u 


o^^h] aQ4iJu 


<4 


»* 


■VX^dv 


afi\^u d^z^M ■ 


30277 


4- 


47 


21 + 15 


2(9 


3»5'9i 


+ 25 


+ 


30 + 14 


31575 




43 


- & 14 


267 


302-94 


36 




33 13 


329- 15 




36 


+ 4 12 


265 


289-53 


41 




12 II 


342 "97 




33 


12 9 


263 


2757" 


39 


+ 


2 8 


3S7" 


+ 


8 


16 6 


261 


261-46 


32 


' 


7 5 


II -88 


- 


5 


15 3 


259 


246-80 


21 




13+2 


26^ 




15 


+ 9 I 


257 


23173 


+ 9 




16 


42-46 




17 





25s 


216-32 


3 




15 - 1 


i%l6 


- 


12 


10 I 


253 


200-32 


13 




10 - 1 


74S7 


+ 


1 


.8 5 


25' 


184 'Of 


16 


- 


3 « 


91-38 




16 


19 9 


249 


1 67 -30 


'4 


+ 


6 -f 2 


loS-48 




26 


- 13 II 


247 


150-20 


5 




13 6 


"5^ 




26 


u 


245 


13270 


-f 8 




15 8 


143-86 




17 


+ 9 9 


243 


"4-83 


20 




II 9 


162 '11 


+ 


5 


II 5 


241 


96-57 


23 


+ 


2 s 


18074 


- 


5 


8 2 


239 


77-94 


16 


- 


7 4 


19973 




9 


+ 3 *» 


237 


58-95 


+ 6 




9 I 


219-oS 




7 


- 2 


23s 


39-60 


3 




7 


23S77 


- 


3 


5 


233 


19-91 


6 


- 


I 


258-80 


+ 


2 


6 1 


23' 


359-88 


- 5 


+ 


3 ' 


279' 16 




6 


5 2 


229 


33952 


+ I 




5 2 


299-84 




8 


- 3 2 


227 


318-83 


5 




4 2 


3»'84 




7 


-»- 1 2 


225 


297-85 


8 


+ 


I 3 


342" 3 


+ 


3 


3 2 


223 


276-56 


7 


- 


I 2 


37' 


- 


2 


3 ' 


321 


25497 


-»■ 5 




3 ' 


25-56 




5 


+ 1 


219 


233-11 







4 


_ 47 "69 


- 


3 


3 


317 


210-99 


3 


- 


3 


■ 7o'o7 


+ 


2 


5 I 


215 


1S8-61 


5 







■ 92-69 




7 


- 4 3 


213 


165-99 


3 


+ 


3 » 


1 i'S-54 




9 


3 


Zll 


143 '3 


+ a 




S 3 


■ 138-62 


+ 


6 


+ 3 3 


309 


120*06 


7 


+ 


3 3 


161*90 







4 2 


207 


967S 


8 


- 


I 3 


P 209*02 


- 


2 


+ 2 


305 


73'3' 


+ 5 




3 » 




4 


I 


203 


49-67 


1 




3 


232-83 


- 


I 


3 


20t 


25-85 


3 


- 


I 


2S6-80 


+ 


1 


3 I 


199 


1-89 


- 3 


+ 


a 


280-90 




4 


2 1 


197 


33778 


+ 1 




3 I 


305 13 




4 


1 


'95 


3»3'55 


4 


+ 


I t 


■ 32947 


+ 


3 


+ 2 1 


193 


289-21 


5 


- 


t I 


I 353*9° 


- 


1 


2 I 


191 


26478 


+ 3 




3 X 


■ 18-42 




3 


+ 1 


189 


240-37 







3 


1 43'<» 


- 


3 


- a 


187 


215-68 


- 2 


- 


3 a 


1 67-63 


+ 


2 


3 1 


185 


191^15 


3 


+ 


1 


■ 92*30 




6 


- 3 2 


■83 


166*38 


1 




^ ^ 


■ 116-99 


+ 


6 


+ 1+3 


181 


141-^ 


■V ^ 


^ 


•i ^ •»- 



r 


r 
404 




Messrs Cotodt and Crommelivt, 


1 


uv^ 


^H 






Tab 


i.B \\\.—<mUinutd^ 


J 


J 


^V 






FottrVi Qmdrunt. Unit o<oooi. 


1 


■ 


^M 


f 


o^XiIn 


tfiXdu 


•liZdu 


« 


9' 


afiXOu 


•nria 1 


1 


179*146 


- J 3' 


- 4 5* - 


I 30 


31*3 


138-731 


33 Si 


1033 


■ 3S7 


178726 


19 


5 50 


I 80 


3" 


134*3<» 


37 04 


Hq 


■ 355 


178187 


+ I 19 


631 


a 21 


309 


129552 


40 83 


iSy 


■ 353 


177-805 


i 97 


6 96 


2 59 


307 


124-469 


45 36 


23 a 


■ 351 


177276 


3 04 


7 48 


2 92 


305 


1 19-052 


50 76 


*7 80 


■ 349 


176 <79 


4 12 


7 88 


3 31 


303 


113-286 


56 97 


31 61 


■ 347 


1 76 '003 


S 22 


8 iS 


348 


301 


107-16S 


6j 38 


33 7« 


■ 345 


175 "229 


633 


837 


3 73 


299 


100-683 


6S 57 


33 sr 


■ 343 


174*344 


7 48 


S 47 


3 93 


297 


93'827 


70 59 


3'3« 


341 


373'J37 


8 66 


8 46 


4 t6 


295 


86-597 


68 39 


2S Si 


339 


172-193 


989 


8 36 


4 35 


293 


78*979 


62 60 


«7 7l 


337 


170-899 


II tS 


8 14 


4 52 


291 


70-972 


54 S3 


187$ 


33S 


169-435 


13 51 


78. 


469 


289 


62-569 


46 38 


31 5» 


333 


167779 


13 91 


7 35 


484 


287 


5376S 


37 75 


35" 


331 


165-960 


1538 


6 75 


4 97 


28s 


44-560 


*S 94 


38 7J 


3S9 


163-921 


1693 


5 97 


508 


283 


34 94' 


19 ^ 


4»7» 


327 


161-662 


IS 56 


4 98 


5 '6 


281 


24*909 


ID 43 


43 4J 


3>5 


1S9'I73 


flo 30 


383 


5 31 


279 


14*460 + 74 


43 50 


323 


156442 


33 13 


» 33 


5 18 


377 


3*598 


- 8 88 


4» P 


321 


1 53 "457 


24 09 


- 58 


5 I' 


375 


353*310 


18 03 


37 J6 


319 


150*202 


26 20 


+ I 52 


4 94 


373 


340-602 


36 00 


31 08 


3»7 


146*670 


28 48 


4 01 


468 


271 


338-470 


- 3a 36 


+ 12 97 


315 


143'SSa 


31 00 


6 93 


4 28 








1 

J 




Tftbla IV. gives for argument u 






1 


I 

— i 
m 


dn I I ' r , 

— — ( ae, — f raCT, — . at 
n m * m ' m L 


-dCJii- J{ 


-e*)} and—; — 


X(2T 




Tlie mecliauical 


quadra tur 


cs for tbo second and 


third quKdrui 




require to be euppi emeu ted 


by the definite tDlegrala arisjng'fnni T 



tpr. 1907. The Perturbaticns of SaUefj'$ Comet, 


405 ^J 








TABLi IV. 




^1 






Fint Quadrant. 


^1 


w 


I to 
n' n 


-> 

m 




Hi 




t 


- "oa's 


+ •0007 


- -0005 


~ 10001 


- 0'200 ^^H 


3 


-a«n 


10005 


-0005 


'OOOt 


^^H 


5 


- "0061 


+ ■0002 


■0007 


0003 


- 0-038 ^^H 


7 


+ X>IOI 


- -0002 


XOIO 


■0003 


0-063 ^^H 


9 


•0283 


•0006 


-0014 


-0003 


^^1 


It 


10478 


-0010 


10020 


10001 


0-300 ^^^k 


13 


-06S9 


'0014 


'0026 


- -oooi 


^H 


15 


'0912 


-0020 


■0033 


+ ■0002 


^H 


17 


■fi45 


-0024 


■0039 


10006 


^^1 


ig 


•IJ87 


'0029 


•0045 


■00 13 


o'ft59 ^H 


3t 


■i6j7 


•0035 


-0048 


-O02t 


11025 ^^H 


n 


•1893 


-0041 


•0047 


•0033 


^^1 


25 


■2154 


10047 


'004I 


•0050 


^H 


27 


■34,5 


W55 


-■0024 


•0073 


^^1 


39 


■2679 


-0062 


+ ■0003 


'OIO4 


^H 


3» 


•2948 


•0074 


-0052 


■01 45 


1-840 ^H 


3J 


■3328 


-0086 


•0124 


10200 


2-013 ^^^k 


35 


■3540 


■0J04 


■D239 


■0372 


3'204 ^^H 


37 


•3926 


•0128 


■0378 


•0369 


^H 


39 


•4476 


'0164 


'0581 


■0506 


3*780 ^H 


41 


■5375 


'0216 


-0841 


■0705 


^H 


43 


■6731 


-0280 


•toSo 


V1966 


^H 


45 


•9340 


•0376 


-1268 


•1385 


^H 


47 


1-4655 


•0555 


■1535 


-2226 


9*043 ^H 


49 


2*1482 


■0710 


■11S7 


■3234 


13*228 ^H 


51 


2-8184 


^0794 


+ -0276 


■4257 


^H 


53 


3-U78 


-0751 


- 10804 


•4844 


^H 


55 


2-9442 


■0623 


-1469 


•4835 


^H 


57 


2-5171 


•0496 


•1563 


■4481 


^H 


59 


2-0637 


-0410 


•12S7 


■4065 


^H 


61 


1-6779 


•0367 


10852 


•3716. 


^^H 


63 


1-3638 


•0355 


-•0364 


'343S 


^H 


65 


l'io3S 


■0364 


+ •0135 


■3195 


^M9 ^H 


67 


-8775 


•0386 


-0628 


•2957 


5-269 ^H 


69 


•6)^ 


■0417 


-1115 


■2687 


4*010 ^^H 


7» 


•4707 


-0452 


•1592 


•2346 


s-Sos ^^1 


73 


•2734 


-niKS 


■2048 


•1907 


1 1622 ^^^k 


75 


+ ^47 


'0533 


•2476 


"346 


^H 


77 


- -1264 


-0548 


•2S57 


+ •0634 


- 0743 ^H 


79 


-3281 


"0561 


■3 "68 


- -0242 


1*931 ^^H 


8t 


-5267 


•0553 


•33S2 


■IZ89 


3x168 ^H 


.83 


715* 


•0520 


•3463 


■2499 


^H 


85 


•8S54 


•0448 


*3J73 


■3842 


^H 


' 87 


1-0243 


•0333 


•307 a 


•5251 


^m 


89 


- rii70 


--0164 


+ •2526 


-•6619 


- «> -if>^ ^H 


J Bam*, -t 


24-3J93 


-'■3575 


^ 3-0688 


+ ys2S9 


•v\«,o-^S ^^1 



^^m 












^ 


^^^ 406 


i/ur/j {^twU amif Crtnnmelin^ 


ucni 


1 


^^ 




Tablr IV.— <CTiii«K«/. 




1 


^^^^ 




Second QtutdranL 


V. only. 




I 


^^^^^^^1 


Li: 

m' i» 


i" 


■ dt 


--^{,-^a-^j 




1 


^^^^H 


+ -0141 


- fncA 


- "OOOJ 


+ •0105 


+ OIOSO 


V 


^^^^1 


"0129 


-\)O02 


'0014 


'0096 


01073 




^^^H 


*loS 


+ \X»I 


10023 


•of>So 


01160 




^^^^H 


"0069 


\>oo4 


•0025 


1D049 


0*038 


i 


^^^^B 


+ "0026 


•0005 


"0022 


+ 10012 


+ owu 


1 


^^^^^H 101 


- •0013 


'0005 


^X)I4 


-•0023 


- DT007 


1 


^^^^H 103 


•0042 


+ ■0003 


- "0002 


•0049 


oxa3 




^^^^H 105 


•0049 


•0000 


+ XOO9 


•0052 


o\u6 




^^^^^ 107 


•0036 


- ■OCXJ4 


'cx)i9 


-•0033 


0*019 




^^K 


- ■0001 


-0008 


'0021 


+ ■0014 


- oioot 




^^V iti 


-t- '0040 


"0009 


+ •0015 


-D069 


+ o*o«i 




^^^^^ "3 


'0069 


- w)04 


- "OOOI 


*oio4 


01036 




^^^^H "5 


•0071 


+ X)001 


"oois 


10102 


0-OJ7 


1 


^^^^H 117 


•0048 


'0005 


'0021 


•0063 


0*014 


^^^^H 119 


+ xx)i7 


•0006 


■0017 


+ \)oi4 


4- O-OOJ 




^^^^^H 121 


- *oaio 


•0005 


- -0007 


- -0027 


- 0-005 




^^^^B 133 


•0022 


+ ■0002 


+ •0001 


■0044 


0''«I1 




^^^H 125 


-OQ18 


-•OOOI 


■0007 


•0033 


o«09 


1 


^^^^H 127 


- "0009 


•0003 


-0008 


- -0012 


~ ofiot 


^^^^H 


+ '0002 


-0004 


*ooo6 


•f-'OOI4 


+ OlQOI 


^^^^V '^' 


'0012 


■0003 


+ •0003 


•0035 


0-006 




^^^r '^^ 


■0017 


- "OOOI 


- "0002 


10045 


0-008 




^^V 135 


'OO16 


+ \MOI 


0005 


•0038 


o^s07 




W 137 


+ -oooS 


-0003 


'0005 


+ •0015 


+ 01004 


1 


^^-_ 139 


- *00O2 


'0002 


-•0002 


-•0014 


- o-ooi 


^^H 141 


-oooS 


-f 0001 


+ ■0002 


■0032 


0*004 




^^m 143 


- -0007 


-'0002 


■0005 - 


-•0017 


- 0*003 


1 


^^1 us 


'OOOO 


*ooo4 


+ •0004 


+ ■0016 


O'OOO 


^^H 147 


+ -cwoS 


- -0003 


•OOOO 


•0048 


+ o-ooj 


^^B U9 


^»i4 


'OOOO 


- '0005 


•0060 


01006 




^^ >5i 


\X)II 


+ •0003 


•0036 


+ "0040 


OiQOj 




I '^^ 


+ •0003 


•0004 


•0003 


, - -0002 


+ 01001 




■ >S5 


- "0002 


+ •0002 


"*0001 


•oois 


- 0*001 




I '^^ 


10006 


- ■0001 


+ •0003 


•0019 


0*003 




■ 1S9 


•0003 


■0003 


•0003 


-■0006 


- O'OOI 




^^^ i6i 


- twoi 


10003 


+ "OOOI 


+ •0008 


o-ooo 




^H i«3 


+ 'OOOS 


- -0002 


- "OOOI 


10031 


+ O'OOI 


1 


^H i6s 


"omj 


'OOOO 


•0002 


10030 


O'OOI 


1 


^H 


+ *O0O3 


+ •0002 


-•0002 


+ •0015 


+ O'OOI 


I 


^^ 169 


•0000 


'O0O3 


'ooon 


-•oooS 


OXUD 


V 


■ 171 


'OOOO 


+ •0001 


+ ■0002 


10023 


0*000 




■ 173 


- "0003 


- '0002 


+ 'OOOI 


-■0015 


— 0-001 




^ '75 


■0001 


•0003 


'OOOO 


+ ■0016 


o-ooo 




^H 177 


- *oaoi 


- "0002 


- '0003 


'0046 


01000 




^H 179 


+ -oooi 


-VOOOl 


-•QOO-^ 


-V-QO^ 


0*000 




^ SuniB, 


+ -Q^A -■ •ooia - 'coq^ 


^-«m 


^ ^'-^V^ 


^^^^^^^^^^^^Bi^HH 


kHBI^fel 


^^■^^^ 




^^^^^^^^^^^^1 




^^ 



Ipr. 1907. 


The Perturhatiom of HaUey'i Comet, 


^M 








TABUt IV.—eoHtinutd. 


^M 








Third QiMdraitt. 


V^ only. 


^H 


« 




m* n 






III ' * 




3^ 


- 


•0075 


+ 'nnn8 


+ •0017 


+ 0065 


^^H 


267 




•0107 


■0006 


+ •0003 


YI089 


0-007 ^^M 


a6s 




*OI32 


"0004 


- '0009 


>7IOI 


o-ooS ^H 


263 




'OII6 


+ •0001 


'OOI9 


>W96 


0*009 ^^1 


261 




'O096 


- •0Q02 


'D025 


•0079 


0*007 ^^1 


359 




■OU64 


*«»5 


*0026 


■0050 


D1005 ^^1 


257 


- 


"0039 


*ooo6 


0024 


+ 10OJ6 


- 0*003 ^^H 


»5S 


+ 


■0006 


■0006 


"0016 


-x»i8 


0*001 ^^H 


253 




■0035 


•OOG4 


- -0005 


inoiS 


0*003 ^^1 


151 




■0044 


- 10001 


+ ■0005 


•oos6 


oxn^ ^^1 


349 




'0041 


+ «»3 


•0015 


^x^fi 


0*004 ^^1 


»47 


+ 


'OOI8 


■0006 


'0019 


- "ooi: 


oxios ^^1 


»45 


- 


■0017 


-0008 


'OQ14 


+ "0041 


- 0*003 ^^1 


343 




•0049 


+ 10005 


+ 10003 


■ooifg 


0*006 ^^H 


241 




•0059 


'OOOO 


- '00 10 


■0099 


0*007 ^^1 


aj9 




•0044 


- ■<XX>4 


0018 


W66 


otxj6 ^^M 


337 


- 


-0019 


'0005 


"0014 


+ 10022 


~ ovoi ^^M 


»35 


+ 


*ooo4 


'0004 


- '0007 


- •0019 


01001 ^^M 


»33 




"OO^ 


- 'OOOI 


+ "tXJOS 


•0031 


coos ^^1 


33' 


+ 


-0013 


+ ■0002 


■0007 


- "0024 


oiQoa ^^1 


229 




*ocxw 


■ocx)3 


10005 


+ -orxi8 


ovoo ^^1 


227 


- 


'0009 


■0003 


+ 0002 


"0029 


- OVOI ^^M 


425 




'OQ16 


+ "OOOI 


- -0003 


•0046 


0*00} ^H 


M3 




"0015 


~'O0Ol 


•0005 


10040 


01003 ^^1 


221 




'OOI2 


'0002 


■0006 


+ •0028 


- 0*003 ^^1 


219 


- 


'0003 


'0003 


'0004 


- 10002 


OiQOO ^^1 


217 


+ 


•0003 


- "0002 


-•0001 


*002I 


OiOOt ^^H 


lis 




•0009 


■0000 


+ •0003 


•0032 


0x103 ^^H 


3'3 


+ 


■0007 


^-ocwj 


"0005 


-•0018 


0*001 ' ^^H 


211 




Xxxn 


*U(XJ4 


+ "0004 


+ 10015 


0*000 ^^M 


209 


- 


■oooS 


+ •0003 


- -OOOI 


•0049 


~ oioos ^^1 


207 




■0012 


- 'OCXJI 


•OOOS 


■OOS5 


^^H 


305 




■0008 


•0003 


'0005 


+ ■0034 


- 010D2 ^^1 


303 


- 


'OOOI 


•0003 


- 'OOOI 


-■0008 


0*000 ^^1 


301 


+ 


xnoi 


- XXJOI 


+ -OOOI 


'0032 


OYtOO ^^1 


'99 


+ 


•0003 


+ •0003 


+ -0002 


- "0014 


+ 0*001 ^^1 


197 




■ooon 


■OOOS 


'0000 


+ -OOOS 


O'OOO ^^1 


'9S 


- 


'0CX12 


+ ■0001 


- 'OOOI 


■0030 


- 0*001 ^^1 


'93 




V004 


-XJOOI 


'0003 


•0038 


COOI ^^H 


191 




•0003 


'0002 


'0003 


+ 0023 


O'OOI ^^^^H 


1S9 




"0002 


10003 


- 'OOOI 


"0000 


- 0*001 ^^^^H 


187 


- 


tXXII 


-•0002 


+ •0001 


- -0015 


^^^^H 


i8S 


+ 


'0003 


+ •0001 


'O0O2 


*0O33 


+ o-ooi ^^^^H 


'83 




'men 


■0003 


+ *OOOI 


--OOOS 


o*aat ^^^1 


ISI 


+ 


*00O3 


+ ■0003 


- 'OOOI 


+ •002^ 


u'aa\ ^^^^ 


9tao7ff, 


- 


•0687 


+ Twro 


- •0102 


+ *Q8a^ 


o'Qiba ^^H 


^^^^^^1 


H 


^^^H 


^^^^^H 


^^^^^^^1 


^^^^^^^^^^^1 


^^^^^■_ -^^^^1 



[ 


408 


Messrs Cawell and Crommeiin, 




^^^ 






Table \y.—*auSinuMl. 


1 


^^^1 






Fourth QModroni, 


1 


^H 


u 


1 rfn 


q" 




•^l.-Vt.-*i>J 


I * 


^^^H 


359 


+ v>35» 


-'OO08 


+ ■0001 


onoo 


oxco 


^^^^1 


357 


-04 >3 


7x109 


*OOOI 


-•onni 


O-ODO 


^^^^1 


355 


•Q448 


■0009 


+ txxii 


■0001 


OIOO 


^^^^1 


3S3 


■04S4 


*OOIO 


- -0001 




0*000 ■ 


^^^^1 


35" 


'0420 


'0009 


^0003 


-0004 


OTIOO ■ 


^^^^1 


349 


■0353 


*oooR 


-0007 


"0005 


own 1 


^^^^1 


347 


•M55 


X]oo6 


•0013 


"ooos 


0-000 1 


^^^^1 


34S 


+ '0125 


■0004 


'ooai 


-oc»7 


o-ooo 1 


^^^^1 


343 


- 0039 


- •0001 


•0034 


-oooS 


Q-OOO \ 


^^^^1 


341 


•0236 


+ •0003 


X)048 


•0009 


ovoo 


^^^^1 


339 


■0468 


'0007 


-0067 


X>oo9 


- OW>l 


^^^^1 


337 


■0740 


'0012 


"0090 


•0007 


OTXtt 


^^^^H 


33S 


•1047 


"OOI7 


-0116 


- XKX>a 


0*003 


^^^^1 


333 


•1396 


*oQa3 


W47 


+ Y>006 


OY)04 


^^^^1 


33" 


•1787 


-0029 


-01 S3 


-0018 


0*007 


^^^^1 


3*9 


'2236 


•0036 


*02U 


W37 


0*010 


^^^^1 


3*7 


■a7i5 


•0045 


'O264 


-0064 


0*013 


^^^^1 


32s 


•5254 


•0054 


X3IO 


X)10>t 


0*018 


^^^^1 


3*3 


•3853 


•nrAn, 


•0355 


■0154 


0^015 


^^^^^1 


3ai 


■4S'4 


W75 


"0401 


V113 


0-033 


^^^^1 


3»9 


•5244 


•noRS 


■0445 


•0287 


0*043 




317 


•6050 


'0104 


O4S3 


•0434 


OT>55 




3'5 


•6949 


■0123 


'0516 


•0589 


0*071 




313 


7955 


'ou? 


■0537 


0787 


0^090 




3il 


■9097 


*oi76 


•0546 


'IO4I 


0'II4 




309 


1*0410 


•0213 


•0544 


•1367 


0-I44 




307 


i 1933 


-02 $8 


■0538 


•1779 


0*182 




305 


1-3689 


•0309 


•0543 


•2294 


o*a29 


* 


303 


]'S646 


•0363 


V583 


-2915 


0*389 




301 


17623 


■0412 


■0683 


*36i4 


0*354 




299 


1-9232 


*<M4" 


■0841 


•4305 


o'4Xi 




397 


1*9955 


'0445 


*0994 


•4861 


o'474 




495 


1*9523 


**H33 


'1032 


■5189 


o-SOJ 




193 


r8ii2 


XI434 


-0866 


•sag* 


o-so$ 




391 


1*6141 


•0436 


-XM90 


'5253 


0*486 




389 


i-393« 


■0473 


+ ■0052 


•5115 


0-4S3 




287 


I'l6l2 


•0532 


■0701 


'4878 


o**>5 




2SS 


•9150 


'0604 


*I4I4 


■4499 


0*343 




a&i 


•6520 


*o68o 


*2»43 


•39*5 


0*263 




281 


370' 


•0749 


-2840 


•3086 


0159 




279 


- -0738 


•0799 


■3449 


•1954 


- o'034 




a77 


+ -2258 


-081s 


•3905 


+ x>S23 


+ O'llO 




375 


•5140 


•0786 


•4149 


-•"75 


0*067 




273 


■7665 


■0703 


■4125 


-3030 


0-414 




271 


+ '^n^ 


+ *DS(lO 


+ -*\\ 


-••Ma 


'^ ^--Pk 


^ 


Siunt. 


- as-79»6 


^i"m*-^^**^** 


'tVSM^ 


_ ^.^ 



tpr. 1907- The FerturhcUiona 0/ Sailers Comet. 409 

In order to calculate the definito integtals artaing from Yg we 
eqnire values of Jupiter's coordinates and relocitiea for U'^go' 
nd U0270*. These are also set down for ua>i8o* so that the 
wo quadrants may be exhibited separately. 





u-90* 


K-ISO' 


u— 370' 


A, 


-3-000 


-1-525 


-3*000 


«.' 


+ 3"ooo 


O'OOO 


-3*000 


«i 


+ 3'903 


+0-775 


+ 3'903 


01 


0*000 


+0-387 


O'OOO 


01 


- 0762 


0-000 


+0-762 


A, 


O'OOO 


-0-0328 


O'OOO 


<Ht 


O'OOO 


O'OOO 


O'OOO 


«9 


-0*0645 


+0*0167 


-0*0645 


3,' 


+02540 


+o'5o8o 


+0-3540 


a,-Bj 


- 0-24S7 


O'OOO 


+03457 


A, 


+0-2540 


O'OOO 


-0-3540 


1' 


-0-5080 


-0*3540 


-o'5o8o 


ft' 


- 0*9672 


0*000 


+0*9672 


ft 


+0-0646 


-0-5083 


+0*0646 


A. 


+ 1-571 


0-000 


-1*571 


■*' 


+ 1*934 


+ 3*934 


+ 1*934 


«4 


+ r"ooo 


O'OOO 


- 1*000 


ft' 


-0-508 


O'OOO 


+ 0*508 


ft 


O'OOO 


+0'I29 


0*000 


I dx' 
na dt 


- o'o7 1 2 


+ 0'5777 


-0-8835 


a 


+0-2755 


-0*2691 


+ 0*2409 


I dj/ 
na dt 


-1-8676 


+ 1 •691 1 


- 1 7005 


t 
a 


+ 0'0I27 


+ o'ioo7 


-o'ii77 


Hence for the integrals arising 


from V3 






tt = 9o'' 


U=:l8o* 


« = 270° 


^ ■ i /''» 


-2-424 


-I -080 


+ 0-257 


bh 


-0'4953 


+0-8218 


-0-4763 


^' f'^' 


+ 2*0296 


-0'i979 


- 1 -398^ 


^> JrfC + V(i-«")Jdw - 


2w-fU f ~ 





+ 2'658 + 2-286 - v'3?''i 



410 Messiv Cowell tmd Crommelin^ 

Heace for ~ > —Idn, 
m nj 

Finfc qnadrsnt 
Second quadrant (V,) 




'rhiwi quadraut (V.) 
Fourth quadrant 

or sulwiituting m' = i 



+ 24-3392 
+ 0584 

+ ''344 

— 0*0687 

+ '"337 

- 237936 
Sum + 3*217 



— j dn= +'00.5072 (le PouU^couIaut— +'003441 . 
Similarly 
/de*«m' - 1*2575 -'0012 + 1*3171 +-OOIO- 1*2981 +1-137 

= Mi' X - o' 1 o 1 3 = - '000097 
|rf(3 = ^ +3*o6fi8- -0094 -3-2275 -'0102 ~ »'2oo9 + 1*467 

= " X +10878= +"001074 radians dd PontiVoolant— +^» 

Ijistly, in order to lulculatu Idl; in extracting th« twoJM 
tlie mechanical quadraturea vve use tbe formula | 

|i{ = |(2r-«0'^+[/A-| I- 7u-^)[y"rfnij_ >/(£. 

in extractiug tbe results of the integrations arising from V -wb sh 
the formula JH 

From the mechanical quadratures 

Jf2ff-n(j-^«"m'l +150*679 + 0-318 -o'o6o-4-36]|' 

= m'x +146-573= ■t-o-i39g47 radians 
Alao 

jrfe -0*746 /dcj = »t' +3'5a59 + 0*0777 + 0-0823 + 

»m'x+q*2jo2= +0008813 radians. 






I 






_Apr. 1907. TU PertuTbiUmm of HaUey'sCvnitt. 41 1 

Henm \dl f part from inwbanicAl quadratures only] 

^ +o''39947 +0*008813 -0*000273 

= +0*148487 radians. 

From the deliuite integrals vre have for —ijdC 
rtegral between limite of I !?{+ J{t-fi-)Llw -^-^^ \dn= - 7041 
— -SlILI — 'x^h^a taken between limits . - =+ 0*900 

■ [nr — rtt\— /ffn at the upper limit 



. viinxw ditto at tLe lower limit 



+ o''5S 
+ 13-767 



Sum + 7781 

Hence Mf (part from intef^l only)= +0*007429 mdiana. 

UetiCH Ute whole perturbation \dl,= +''559^ radians. 

It should l>e stated that eererat Approximiitions hare been 
[intTodiiced ; io particular the square of the mass of .luplt(^^ has 
[been neglcctei), ur iti uther words the tliaturbin;; forces hare been 
tcomputed as if tlie comet was in ti certain mean iindistur1}cd palh. 

Our ro-siiU for Ids Is one fifty-fifth part of that given by 

rde Pontecmiilant, C.R.^ Iviii. p. 827. ThiA renders it extremely 
[probable that de Fontt'coulant'a error consisted in the omission 
I of tbe factor, circular muasurv of one decree. 

Dfi Pontticonlaut'ij valuu of /t/£ is + -15303 radians; this 



implies that, cunsiderinp Jupiter'? action only, his value of the 
,next periheliuu paasago is thirteen daye lati;r than ours. 



4I» 



Maffniivdt of o Ceti (Mint), as observed LXiud 



iiagfUinde of a Ceti (Mira), 1906 Ihfetaher 14-1907 F^irtmrf it^ 
cu obaeTve<l at the Raddife Obgervatorf/, oi^urd. 

{Ommunimk&i by the Radclifft Ottervtr,) 

liLfurniutiou haviii;; been received early in December thtt tU 
incrcaae id the light of ^Mira C«ti suggested a m&xinitim vf abaomd 
brightness, obRorvations of this variable wero undertaken W Hr 
Wicltham and Mr Robiiwon. 

The.se ubservatioiiK are made by Argclander'a method, and lit 
all imkeii-i^jT'c estintations. 

When the oMtrvutioHa commenced the variable had aln»Jt 
considerably exceeded iu brijjlitness on the occusion of the lut 
maxinmm, but a ctirve drawn to represent the observed magnitoite 
does not clearly indicate a maximum, the epoch of which m^ 
have occurred previous to December 14. Unfortunately, obserratiinB 
were renderf^rl impracticable on December 11—13 by bad westfaff 
which prevailed. The date of maximum derived from Oh and W* 
" Revision of Eleuiients of Third Catalogue of Variable Stan" (A. 
553) i» igo6 December 19.* 

The vtiriable was so bright on the earlier night« that it 
necessary to tike companBciii-«lars situated atconaiderabledis' 
from it, and at various altitudes, but these are distributed in 
a way that the reaulting mean will, it is hoped, be fairly free fi _ 
the effects of atmospheric absorption. The proximitv of a Oeti, 
the colour of which was similar to that uf the variable, was fn mw< 
advantageous, bul the obnervers met with tiiv usual dilHcnltv j^| 
comparing the dull yellow light uf the variable with that of losUoV^ 
white stara. 

Some notes on colour are included amongst the *' O 
Remarks." 

It is worth mentioning that in the Harvard Annah^ Ph<Ao 
vol. xiv. p. 13 1, a Ceti is described aa *'0," or pronounced 
whilst in the rccuatly publiafaed vol. xvii. of the Potsd&oi Aatt^ 
physical Observatory this star is characterised as " Cr~-,^ or batnaw 
light yellow and yellow. 




»baert«^ 

O/ORflfl^H 



I 



' It may be veil to point out here that th« Moond tenu of the 
iiicqimlity on givea in we footoot* tu th« catalogue a iacomctlv 

The oo«fBct«nt »hoaU b« 11*3 ^'uot tx'^j , t1i« unit being a day. 



Apr. 1907. at the Hadctiffe Observatory, Qx/ord. 



4U 



Taiile I. 
Stars vnd for Cbm^uirifm. 



FuiK tA !^Ur. 



NP.D. AOupUd 


6'r 28 


215 


75" 


3-87 


to8 32 


3 '26 


29 49 


2-25 


10043 


3-61 


54 55 


J-37 


9842 


3-83 


75 '" 


3*7' 


6941 


273 


8743 


3 '94 


489 


3 20 


671 


2-23 


81 59 


4'34 


906 


400 


8711 


3-58 


9918 


4'o6 


86 18 


282 


4926 


2-31 


9911 


4*88 



R«r. 

No. 



20 
21 
33 
23 
24 
25 
36 
a? 

3J{ 

29 
30 
31 
32 
33 
34 
35 
36 
37 
38 



Nmme nf HUr. 
B Panwi 

S KrirUni 
7 EriilBtii 

AlticlMinii 
t Aurigw 
fiErwlAui 

Eig«l 
7 Orionis 
flTauri 
S OrioDu 
• OrionU 
i Ononis 
K Onouii 
aOricnis 

0P«Kut 



RA. 
1900. 

h m 
3 '7*2 
3 28-2 

338-5 

3 534 

4 30*2 

4 50-5 

5 29 
5 97 
5 19-8 

5 20X} 

5 »6'9 

5 3'' 

5 357 

5 43'0 

5 49-8 

5 Sa-2 

30 i8"6 

22 58-9 

22 598 



N P.D, Adayloil 
190D. Mac. 

4030 190 

9948 
1006 
10348 

7341 

57 o 

95 '3 

9819 

8344 

6i 29 

9033 

91 16 

920 

9943 

8237 

45 4 

504 

6228 

75 30 



The adopted rnagaitudea iire tfai4 tiiBiins of all values found iti 
the rollowing Harvard Annai*: — 

1. "Harvarii I'hotometry " (vol. xiv.). 

2. "Photometric Revision of the r>.M." (vol ixiv.). 

3. "MiBoellaiieoua PhotoiiLotric MeaeurfmuiiU" (vol, xxiv.). 

4. " Pbotoinetrb lleviaioo of tlio Harvard Photomoiry" (vol. 
xliv.). 

5. "A Photometric D.M." (t«vI. xlv,). 



3-»7 
106 
2-86 
3-87 
o'34 
170 

17S 
2-48 
i«8 

1-89 
318 

0-93 
307 

3-32 
2 61 
357 



P«Twi<l Hwtr. 


our. 


1906. h 




Dct 14 7 


R 


'4 9l 


W 


31 %\ 


W 



Tadlb 1L 
O^rwiiot^ uf Ihr ytaynitude of • Ctli {Sfira). 
■itliiMtioai, 



•2 [29; 'I b 12 ; •4b 17 ; =3 

niii'.-h r34, 30, 31, 32, 35 ; much b 10 

= 18 ; = 1 1 ; 5 1 12 i -33 1> 17 ; 67 f 35 : 
'5130, 31, 33; I'jbio ; mocb f 24 

•2f29; -aruj ita 7hi7; "7^9 



RmuIU 

UftfDltU 



3 '19 



2-^ 

■x\t> 



V2. 



4<4 



Mmjnitntk of o Ceti {Mira), as observed li 



TablB W.—tenlinued. 
(MmrvtUwM of tho MasnUude of o Oeti (MiraX 

■MlBHtkHH. 

•jriz; '25630; -asfsi ; •isl^a; =11 : mt 

r 24, 27, 34 
■3f 12; -511 17; =31, 3H -jbjo; -a li 11 

= i2;'2fi ; -31.38; rbs;; 7^17; =38(ind 

obs.) 

•zf t: -2 fix; -61)9; '♦bi? ; '4f39 

•3bi7; •4f»38; •if37; "filig; 'Sf i ; -jfJ*; 

■61)2 

■3fi j=6, u, 12.36; ^bi?; -jfaoj -ar35 

■3bl7; •3fr2; -ebj; -3(6 

■5faS; ^f 12; sbg; ■3faoj*a5bi7: •3r36, 

35; -2 f 29. 30; 1 b4;=33; H« + ») 
■Sb9 ; "S fix; -i b 17 

•4f 12; -iby; -3(6: 2 b 17 ; afja ; 'a b 55 
= 17; 4(9+11) 

•25b9;'3fi7; •5b2; if-ii, '4 b 26 ; '5623 
■iSfl7i •2)k); 31.2; *4b26; -3 f 30 
■4fi7; ■3''2J: ab2<i;*4f33j '865; -987; 

l-obiS; ^fjOi ''5''* 
■2 b 26; -4 (33; -4(17 

= 26; sf 17; ^SbiS! •2r9: -I fas; IfS}'. 

•i f 2; -8 1*10 

■2r23; -abist «( 17: •3»>to; = 36: ^sfij 

■55f9t ■3ba2; Hbai; ^b 14 
■7 f 17 ; -25 b is; -5 b 14. 10; A^xO, 21 ; 4 f 23,8 ; 
'I3b32; 'jftf; *2f26; '3 b li 

rofi7; i(l4 + i7) 

= 16, 2t ; -3b 14; 'lb 10 

■If 14; ^f 10; 2b 13; -6 big; 'zfie, 21 

tnuvh f 14 ; esliinated mag. 

Observers Retnaria. 

1906. Dec. 14. Half weight to oomparisoD with No. 3. 
of Mira a mean tint between the pale yellow of CapeUa and 
deop orange of Ahlubantii. (R.) 

(Willi rtuiuU tuleacojie, aperture i j-iiich, the image of tba 
allowed distiiict carmine fringes, wbiuh wore not visible in 
cnnapariflon fttarfs, with two exceptions, a Cell ami Aldebaimu, when 
thfi colour and fringes were much fainter. [W.]) 

Det^ 21, 2*]. 'VUi "JiuW 'ijisW^'w wi\<iu\(A u\« variable and am 



D«r and Boar 


UtM 


1906. 
Doo. 36 


fa 


W 


27 


SJ 


w 


27 


84 


R 


1907. 

Jul. 2 


64 


K 


3 


6 


K 


3 


61 


W 


6 


8i 


B 


6 


84 


W 


11 


6 


B 


II 


7 


W 


17 


8 


W 


17 


84 


U 


18 


7 


K 


22 


7 


R 


23 


64 


K 


«9 


7 


R 


3» 


6i 


R 


Feb. 3 


63 


R 


3 


7 


W 


10 


8 


U 


'J 


7 


R 


16 


7 


R 




Apr. 1907. at the JiudcHJfc UbstrwUor^, Oxford. 



4i5 



of tht! CfimiJiiri.-jiin staTn is ubvioiw to the imked eye, and comimrison 
with brilliant white stan, such as those of the belt uf Orion, ia 
difficult. (W.) 

l>ec. 26. Observations rather dtfl'icult owing to the proximity 
of the Moon. Slight haze at times. Half weight to cumi«rison 
with No. 3. (U.) 

Ufc. 27. Mira ."tiniilar in colour to a Ariotis, yellow. (K.) 
Half weight to compiiriflon with No. 17. (W.) 

1907. Jan. 2. Colour af o Ceti similar to that of a Arietis, (K.) 

Jan. 3. a Coti is reddish; Ceti is yellow, closely rciwnibiirijj 
tt Ariftis in colour. (R.) 

Jan. 6. Colour of o Ceti same as a Arietis, but a Ccti and ^ 
Aiidrom. are orange-red. (K.) The yellow rolour of Mira is still 
manifest to the naked eye. (W.) 

Jan. 1 1, a i^vix reddish ; a Arietis and a Ceti yellow. (R.) 

(W. iind U. exaniirieil Mii-a CetJ with the Barclny K^iualorial, 
ftjiertun* lo-inrh, pnwpr S8. Koth observHr» noted that the iiuage 
of Mira idiuwtd mar!ie<ny n'd sjiicut^v nrouiid tbL> umrgin, but thin 
Ulurgin n-ati not so broad nor so deep a r»d u-s the same observers 
saw arutuid Xava Pcraei in igoi. Two oilier coluured stare were 
Gxamineil for comparison, a Ceti exhibited but little red in ite 
fringe, whilst a light orange ur canary colour prevailed over the 
main image. Aklebaran showed reddish orange with a narrow 
margin of red, but tliiti of u light tint ouly. The iiijiiye uf Mira 
Ceti wtk- tbt-refore quite distiuct in uppuumnce from these stars 
wheu viewed with the sume optical means. 

Observer R. uoten, in addition, that "with the naked eye Mira 
in not so deep an orange as a. Ceti, but with the I^arctay telescope 
it is decidedly dirt.-|H-r than n and out quite su bright"] 

Jan. 17. Sky itself iruiispitrently clear, but a ground fog pre- 
vailed, diminishing from the horizon tuwiirdi) Cetus, but even 
there it obscured all stars of the fifth mftgnitiid*'. (VV.) 

The fog seemed to render stairs of an orange colour more 
conspicuous to-night ; a Ceti was, probably from this cause, 
relatively brighter thitu hbuuI. The observations were made from 
the summit of the Observatory tower, 100 feet above the ground. 
(B.) 

Jan. 1 3. Foggy; e>4timntionR diBicuU ; hut ]hrohably the mean 
is reliable. Tlie olwcrvatious W4>rc uiado from the summit of the 
Observatory tnwvr. (R.) 

Jan. 22. Bright Moon eti'ectually screened during the obeor- 
vations. (R.) 

Jan. 23. A brief comparison only. (R.) 

Jan. 29. Observed in intervals of vloml and tu bright moon- 
light. Estimations rather diHicult, but mean is reliable. (R.) 

Jan. 31. Sky hazy ; observation dilticuH. (H.) 

Feb. 16. Seen with difficulty in moonlight and through low 
haze. (R.) 

Rmldige Obatrvalory, Oxford: 
\<fyi Ayrii 9. 



4i6 Mr W. F. Denning, Ettrly ami LaU Perseidi. 

EaThj and Late Pmttidt, By W. F. Denning. 

The following is a list of the apparent [taths of [>rut«b)e ul 
[lossiblu Pui.itekU <jl)!iflrved at Bristol during the t6 nights Jolf ; 1* 
22 uiid 9 uigliiB August v^ to 25 iuclusivt' ill the thirty yean f jcb 
1876 In the |>resent time. A [^iroijortimi uf thij»iu mt:t«)pi »« 
undoubtt'JIy not true PerseiJs, Iiut beloujcrd to the other sbcnrw 
oxistiiig in Cassiopoiu, Audroiacdn, Pihccb, Aries, Caiucli^n:« 
Tniirufl, Auriga, etc., at t\\v. ftame e[>och. There nro ft ^eat numW 
of such ratiiauts vi^iiible — ctTtaiuly more than a hundred — and itu 
rury dif&cult to attribute eurrfict positioiia for some of the individail 
meteors which have appoared at this time of thu year. 

The raateriaU here liirnishcd may aifbrJ some help in detenBia- 
ing th<j datu-4 of begiuiiirig and ending of the Ptrr«oid BboW 
These HTo very doubttul at prtiseut, but 1 believe that the vtiijtb 
of L'vliU'Mcc riivours the conclusion thai truu Pen»id« majr b 
occasiiiDaily recogriiiMid nfior the first week in July. The disph? 
is very feeble at t)tat tima, and may not supply one meteor durni| 
a watch of ueverii! liours by a single observer. But on Jqiy 19 
the stream becouitM well [iroiiouiicttd, and its mdiant ciiiubli' >^[ 
being definitely ascer'ained, though nut in every yaar. Tbi! d«ti 
just nteutioiiud is in fact the earliust one on whidi I can cx>nflde&t(i 
say that t'er^eid meteors are itoroetiiiies viaible in suflicient nunibm 
to enable a ^<iiid radiant to be obtaiued by an individual oboc-ver. 

In the lust t^ulumn of thu list I have ascribed the radiaiiu » 
thoy appear in uiy MS. book^ of obsetvuiittni). Theae poaitionii m 
notnnrrect iti all v.aAi>ti. Itut I have reprojectfid tln^ apparent patbt, 
and have aliixed the letter V to diatinguisb those which msj U 
regarded as Perseids. 

If other observers will supply similar data it will be posaihle U 
deduTO the place of the radiant oti every night fn>:n July 7 to 
32. But It cannot bo safely said that the showur begins mi eari; 
as July 7 : it will be very ditticult to learn when the earth realJ| 
encounters the Hrst shots from this widely •distended stream. 

Further luutetiuls for the above period, and for the coiiclodini; 
stages from August 17 to 25, will throw an inton:sliiig li^ht on 
actual duration of the shower, and on the positions of the 
near tha limiting dates of its visibility. 

We might soon iletermine these features but for the iv\ 
there are many other secondary displays yielding similar mi 
and radiating from the same re^on of the sky. It is often tai| 
sibli! to »uy whether ineteorit are Pereeids or nott thonah 
flig:ht-<iirectic)ns may conform with the position of the great At 
shower. At the earlier stugOi) of the display there are well-dc 
tuiuoc nuiiaots at about 



»3 + 43 

2J + 57 
29 ■» 36 

33+ »S 



33+ 5« 

43 + « 

44 + 57 

47+43 



SO +31 

60+58 
614^48 



— and many othere, \MTjw^m*\,TCii.'t^Vw>m'Sft»s \*> ^ear. 



^ Apr. 1907. Mr W. F. Denning, Early and Late Perseids, 417 

With regard tu the civncludtn^' phaseit of this systetn, I Iiave 
recorded nieteoi-it from the right |>ONittD:i u\t tit AugiiAt 35, but 
there ure douhls as to whetht-r llie ghowor is really prolonged to 
that Jute-, It ia certainty continued to AugUfit 20, but on KuUie- 
quf^nl ni^bia the evidence gleaned is nut sufficioiitly ample to 
enable one to Almohitely afhrm its vieibtc continuance. From a 
i discussion of my ctirubinod obsorvDtiims in variotia years, 1 have 
detiuced the following radinnts nf i'eraeids : — 



Aug. 16 


53 + SS 


21 J,s 


Aug. 30 


57 + 59 


10^* 


.. 17 


54 + 60 


s.. 


M ai 


64 I 59 


12., 


tie 


55+59 


II M 


.. 33 


70 ( 61 


7m 


.. 19 


57+59 


S'. 









Onnpanion showers (in addition to tho^e above given for tbe 
earlier stugea) iire well prouuunc^^d ut about — 



39 i 28 


70+66 


75 + 15 


5«+ 9 


71+ 5a 


77 + 3* 


61 +36 


74 + 42 


87 + 43 


63 + 32 


77 + 5S 


id6-»-53 



The enrlieet radiant I have ubtaicted, presumably fur the PerseidK 
(though a shower of Cnssii^peids may ula" l>e involve^]) i.s fnr the 
period .July 7-9, 10' + 45 4 , ten meteors, <^uite possibly the shower 
continues ^luring lifty ni^Iils July 7-Angiifit 25. 

The LBt« Mr J, KLnibpr gave the theoretic^] phtce of the Pereeid 
lia.nt a«, on July 3, 9° + 46*, and August i6, 54" + 59"— (J/onM/y 
lii. p. 35 i). 



Observed Faih* 0/ Knrty Ftntuls. 



From 



Td 



V%Ux. 



XOtM. 



349+25 
318 + 55 
240 + 61 

47 + 71 
61+594 
355 + 33 
332 + 72J 
310 + 30 
339 + 2« 
378 + 45 
344 + 58 



345 + «> 
«Sj + 49 
318 + 37 

87 + 73 

81+70 

349if + lOj 

3»+7S 

3«3l <• 14I 

31613 

360+32 

334 + 59 



RK P 

RK P 

vR it K 30 + 11 

R 345±o 

BK 

RK P 

ait K P 



11 49 4 344 + 594 3J3 + 6ii 6 



au.' 



[ 


41S 


Mr ir, F. Denning, Early ami JUiU J^rrseid*. 


m 


H itmu. 


U.M.T. 
h ni 


nwjc. 


rroni 

'Z % 


To 
■ t 


P&Ui. 


Knla. H 


^B>9°4 


July II 


14 14 


2 


18+36 


204 + 3*4 


4 


K K 


r 


■ ^1877 


IS 


II 43 




335+48 


313 + 40 


17 


& 


47- 


^^H 


II 


II 57 




33b + 30 


3'3+i' 


lit 


V K 


p 


^^P 


II 


12 17 




J40 + 64 


308 + 66 


13 


r RK 


«J 


i8S<i 


It 


11 lb 




2SI-15 


275-214 




S K 


f 


1S8S 


11 


'a 5 




44 < 58J 


54 + 60 


b 


KK 


p 


1S85 


'^ 


12 9 




2934+354 


376S + 30 


31 


T RK 


p 




ii 


12 49 




356+41 


350 + 374 


6 


K K 


p 




14 


<2 35 




324 + 64 


279 + 63 


30 


V R BKP 1 


[901 


J5 


U 5 


> I 


370+53 


3484+32 


24 


K K 


2J'I 


1876 


16 


ir 17 




260 + 80 


225 + 67 


'5 


KK 


n 


^_ 


»i 


'I 33 


.1 


310 + 5* 


286 + 35 


33 


t K K 


^i 


^^H 


>i 


12 19 


3 


321+42 


304 + 30 


'7 


U B K 


p 


1S9S 


.. 


11 4 




24^53 


26+57 


4 


SK 


p 


1903 


■ • 


13 47 




•Si ^55 


144 ^ ss 


3 


RK 


XOi 


tSf^ 


ti 


12 12 




34» + S3 


539 + 534 


51 


RK 


*3^ 




•1 


13 42 




8 + 66 


0+71 


6 


SBK 


23+ 


1898 


'7 


E2 42 




25i + 54i 


37 + 59 


5 


U K 


33 ^ 


1876 


18 


10 35 




16+47 


15+40 


7 


R 


*7* 




>( 


1: 20 


>i 


211+49 


206+18 


31 


RK 


P 


1S81 


If 


11 9 




110 + 70 


144 + 5S4 


19 


KK 


P 


1887 


■1 


11 ) 


> I 


3 + 34* 


+ 31 


4 


SBK 


P 


1900 


II 


10 38 




314 + 4*1 


306 + 42 


S 


RK 


P 


1S76 


■ig 


10 5t> 




346 + ^5 


337 + 1" 


10 


B K 


r 


1887 


>* 


II 43 




358I+38 


351+30 


10 


SBK 


p 




„ 


12 35 




350 ^ 62 


3304+64 


10 


SBK 


p 




'1 


13 S 




356 + 47 


347 + 44 


7 


UK 


p 


1900 


t., 


II 43 




344+33 


339+18 


30 


RK 


p 


(901 


11 


II 41 




335+68 


289 + 67^ 


134 


v k K 


33 + 




>, 


12 sb 




346 + 35 


5394 + 30 


7 


RK 


p 


1876 


20 


tl 29 




341+6 


335-8 


15 


K 


p 


1901 


91 


11 24 




338 + 60 


303 + 584 


8 


V RK 


33-4 




• 1 


II 59 


3 


328 + 59 


393 + 54J 


30 


* RK 


33^4ij 


1876 


21 


11 21 


2 


344+60 


3'S + 57 


<S 


KK 


' 1 


18S7 


•> 


13 40 


3 


5 + 44 


3594 + 39 


64 


V R 


' 1 


^ 


^ 


" Ob^srvvl &Iso l>j J. Lucas., Oxford. RaJiuiit, 2a'+ 5/ 


J 



Apr. 1907. Mr W. F. Denning, Early and Late Perseids. 419 
Obierved Paiht of Sarly Ptrseids—eouHDued. 



Date. 




Q.M.T. 

h ID 


mag. 


From Tc 

at a 


Patb. 


Notes. 


1 901 July 21 


II 


57 


5 


53 + 624 '70 + Hh 8 


KE 


23+43 




tt 


12 


2 


5 


25+36 25 + 


32 4 


RE 


23+43 




i> 


13 40 


3 


311 + 52 2974 + 


45 " 


RK 


P 




,, 


13 43 


1 


349i+»5 34» + ii »6 


RK 


P 




ti 


M 





3 


26 + 53i 31 + 


53i 3 


SK 


P 


1887 


22 


II 


2 


4 


6 + 43 1+40 5 


RK 


P 




)■ 


13 


21 


V 


356+45 332 + 29 24 J 


R BK 


P 




1 1 


13 


2 


5 


25 + 47 27 + 43 4 


3 


P 




»> 


13 55 


3 


33 


1 + 77 281 + 


75 12 


RK 


P 


1900 


1 1 


II 


IS 


2 


13 + 55 356 + 


59l 10 


SE 


P 














LaU Perteids 










Dite. 




O.M.T. 

Ii m 


nug. 


From 


To 
« i 


Fatb. 


NotM. 


1901 August 17 


'5 


21 


2 


90+43 


98 + 35 


10 


R P 


iSSs 






iO 


59 


4 


346+59 


318 + 46 


21 


RK P 








12 


44 


4 


3044+46 


2984 + 39 


8 


vRKP 


1898 






9 


36 


3 


554+69 


574 + 74 


5 


8K P 


1899 






15 


8 


2 


96+43 


103 + 36 


84 


RK P 


1885 




18 


13 


37 


3 


335+37 


328 + 271 


II 


RK P 


1893 






12 


25 


9 


330+31 


3154 + 9 


36 


RK P 








12 


37 


I 


38+10 


374 + 1 


"4 


RBE P 


1901 






10 


28 


3 


327+40 


320 + 21 


23 


BK P 








10 


54 


3 


329+50 


313 + 344 


17 


RK P 








II 


44 


3 


241+84 


236 + 72 


12 


REP 








12 


16 


5 


44+10 


+ 2 


9 


R P 








12 


48 


5 


69+634 


83 + 654 


6 


RK P 








12 


53 


2 


37+644 


25 + 66I 


54 


SBK P 








13 


4 


2 


345+86 


236 + 71 


15 


RK P 


1884 




19 


II 


10 


3 


88+59 


92+594 


24 


vR 77 + 58 








II 


27 


3 


39+68 


23 + 70 


6 


K4' P 








12 


21 


4 


341+784 


308 + 73« 


9 


BK P 


1 901 






II 


48 


4 


3534+16 


348 + 9 


9 


RK P 








12 


29 


3 


224+584 


14 + 57 


5 


SK P 


1885 




20 


II 


41 


3 


28+46 


24 + 43 


5 


RK P 






■ > 


13 


55 


3 


3524+15 


3474+6 


10 


RE P 



^^L 420 


Mr W. F. Dinning, Early a 


Uf^ Xa<« PeramtU. 


ucntti^B 


^^^. 






LaU /Wwriif* aontiiiiml, 




J 


^^^^^^F 




O.M.T. 


fVoB 


To 




^H 


^ H«e 




b « 


m«ic- • « 


r**« 


PaU 


"^ 


^B 1887 Augiwt so 


10 1 


5 356 + 67 


397 + u 


64 


8K 77Trf 


^H 1901 


ti 


10 16 


- 1 349 * 43 


3271 + 194 


39 


RBK P 1 


^1 


(» 


10 35 


3 79 + 5*4 


92 + 53 


S 


8 P 1 


^B 


!• 


It 2 


4 3S) + 23i 


*54 + <s4 


» 


8 P 


^^^^^^ 


>t 


11 41 


3 72 • 674 


83 + 71 


5 


SbK P 


^^^^^f 


• I 


" 45 


5 3574 + 324 


350 + 33 


11 


BK P , 


^^^^^^ 


t« 


IJ 58 


4 3084 + 50 


399^+40 


>t4 


E i|^ 


H 1884 


31 


II IS 


3 16 + 56 


3 + 54 


8 


KK 7'!^ 


^1 


t> 


II 40 


3 4« + Si 


309^84 


II 


RBK7t »53, 


H 1887 


•f 


10 3; 


5 " + 504 


0+44 


10 


HK 77 + 5« 


H 


■ 1 


la 58 


4 ^+49 


18 + 454 


7 


RK 7lUd 


H 1901 


• t 


10 D 


4 3'»4+5'4 


303 + 41 


13 


RK pH 


^K 


t» 


la JO 


3 14*45 


359*^334 


■ 5i 


BK t^M 


^^^^^^ 


• > 


12 48 


1 33) 4 17 


16 + 34 


«$ 


RK P^l 


^^^^^B 


•( 


»3 8 


4 I7 + »J 


114+3 


•3 


BK rH 


^ 


.. 


15 " 


S 66-^36 


66 + 31 


5 


BK P^ 


H >903 


M 


13 4 


♦ 30 + 374 


37 + 33 


54 


BK P 


H 1884 


32 


13 3t 


4 7» + 48| 


69+434 


^4 


aotBK 77 +-£11 


^1 >9°0 


«i 


ID 90^ 


3 387 + 784 


364+67 


13 


<rSE P^MM 


^^ 


• I 


11 39 


4 .74+38 


11 + 17 


'3 


RK P^l 


^B 


■I 


11 48 


3 »'+44J 


3*374 


8 


RK l^l 


V >90l 


«• 


10 53 


4 334 +6a 


3'9 + 524 


13 


UK P^l 


^L^ 


'» 


<» 5 


3 114 + 10 


7 + 3 


9 


RK P^^ 


^H||b6 


«f 


II 8 


.- Jf 18+38 


74 + 38 


»3 


SK P 1 


^■^ 


.. 


11 9 


5 345 + 33 


336 + »2 


•5 


rRK P 


^1 1^ 


aj 


u 59 


I 345+ '9 


3354 + 2 


'94 


»BK40 + 5» 
BK 7*««» 
B 77*58 


H )1%7 


•t 


13 37 


3 9J + 6»4 


1094-601 


8 


190D 


1" 


n I 


4 16 4- 33 


13 + 16 


7 


1903 


ft 


11 


4 35 + 37 


23 + 21 


7 


notRK 70 ^65 


18S7 


»4 


II 10 


3 66 + 70 


6*Sil 


•74 


BK 77«Slt 


^ 1900 


It 


9 >6 


3 35fJI 


to + 43 


i3 


»BK 77*5» 


V 1179 


»s 


II 


3 243+30 


34 j8 * 16 


14 


BK 61435 


'903' 


•• 


9 35 


3 37 t *> 


30 + 19 


13 


RK 79+59 ^ 




a, tlow ( B» brifkt 


, K, iliMk i » 


. Wfyj 


T.rmtbL 1 


^ 


* AIm oImtv**! I7 Mr a L. Btvok ftt MolUtani, Huddtnlldd. ^^^Jl 



Apr. 1907. SUclric ArrangevMnU of an OhMrvato7'y. 421 



Tkt SUcMc Arran^nmtn of an OhntrwUory. 
By W. Ernest C;ooke, M.A. 

A syatoni of oluctric connections for the iiumeKua iuetrumcnts 
has been evniveii at the Perth ohsorvatory ')f so nimple and con- 
veuient a character that a deacriptioa may be intureating and perhaps 
useful, eapeciaUy to those who ooti tern plate eslHblishin^; a new 

^observatory. 

There, is only one sidereal clock anil one battery aned for all 
purpotiea, Kuch aa chronographa, dock dials, cluck control, equatorial 

>^ooiitrut, cbrouuKi^ph control, tmii^it keys, aud email elcsctrtc lighle. 
Tbo l>attvry cotisisbt of two large ncuumulator eolls having an 

iJiLM.F. of 4 volts. There are in reality two of these used alter- 

[nately, ao that one may be always available. It lit lound advisable 

Flo change the batter)* at 9 a.m. duity, and tu recharj^e the one not 
ill use. The cliar^'iiig ia ptirfuruiL-d very niiiiply by nieaim of u 
motor trausfoniier, worked frm Uk* ordinary electric U^ht supply 

'current 

By raeona of a three-way switch either battery can ha turned 

|-on or otF, or conuected with the chttrgioK transfonuer, instantly. 

From the battery a pair uf heavy maius ore run round the 

^buildings and connocied to a pair of terminals in eucb room, wherein 

fftny instrumeiiU which require an electric current are locited. 

'Tlief^ terminals are Isbidled A and B, 

Frnm the contatits of tlm siilureal clock a current pfutstts thnmgh 

' a relay, and the contacts made by the armature of this relay practi- 
cally tnJical't' the adopted KecondH r>r tbc clock. It has bwn con- 
aiderod advisable, in the case of thn clock contacts only, to use a 
separate battery, and two cella uf the ^'ravity type are found t«i 
giv» Mulficieut currents But even in this case a switch Las been 
ptDvided for subatituting the current from A B if the gravity 
battery is out of order. 

One of the tpviuinuls of the secondary contact of the relay is 
connected to A, and the otber to a third main wire which runs 
round nil the )>uildiiigs uud is labelled C The fiuictton of the 
clock relay is thus to make a niotaentary connection between A 
and C at every lieat of the sidereal clnck. 

We have thus, in every in.'itrument room, the three terminals 
A, B, and C, and from ihetw all uecL-^uary conueutioun can be made. 
Thus, for a chronograph or clock dial, wires must be mu direct from 
C B, and thiA gives an eli^ctric impulse every second, nince C nnd A 
are joined once a second by the sidereal clock relay. For an 
instruDieut whicli works by lueaiis of a key, or any form of hanil 
control, wires must be run from A B. if a chioaiy^TavV \m qV n. 



422 



Mr W. Bmat Cooke 



UTIL^ 



single \»a typti, i.e.. if buth the clock beaU aod the fc«y Ufa iff « 
be regititered by meaiu of the Mtac eloctro-inagnt-t, it will k 
Deeeaeary to introiluc« a relay ; for otfaerwisu the key will maoid 
A and C, anrl will fi^nd an extra impnU^ along the rlock circuit d 
every tap. In \\ih csj'e the primary termmaltf nf the nU; m 
cuiinuc-ied wilh C B direct, and the uucoudury with A B thra^ 
the chriitingraifh. Tb<; aecoiidary ol the relay i» thus pUord a 
pamllcl with the kt»y. 

It may be mentioned that one of tbew) i-claya ia used as a 
for transmitting clock htiatx in determining' differences of It 

The aygtem is especially coDvcnient when it ie desired U> 
trul an inslruniont in one building by means of a kej or 
mcnt in another bailding. For instant^ thero is a clock dial in tb 
transit room, worked fnim (he sidereal clock by simply cooaectiis 
its terminals with B C. ThU dial contains a pair of cuatKQ 
which are juin^Hl for n ooiiplir of ttecunds at eacli sidereal hoar. 
These are raiiiired tji control, by me*ins of Luud's chpo, a tkA 
keeping nidt^real time in anotlier bnildin^. The cuuDectiou «* 
verj- simple. One nf the primary contacta of the dial is aliWi 
connected with B. It IH now also joined to ont* of the sc 
contacts. The other secondary is connected to a sin^de line *l 
which leadK to ona of tbo terminals of Land's control, and tic 
other terminal is joined to the nearest A. The arrangement 
shown in the diu^mm. Even the line wire might be dii 
with and an earth iiood if this instrument only were conoer 
but it will be found ndvienble to keep away from earth cunnectidw 
entirely. 

The accompanying diagram givea a rough sketch uf the mamxt 
in which the sy^itcui ia uaal, but conveys no idea of the number <tf 
ioatruniente winch may bo i.-onnected. At the Perth ObaerraH-Tj 
the following are all worked by the one battery :-^ 

Two sidereal dials, 

llirec Gidi'real chronograiihe. 

Unp mean time thronograph. 

Three transit keya. 

One complete looKitude systeni for short diatanoea. 

Ono Lnrid'a controHe-d clock. 

One mean tiino multiple relay. 

One electric ri>ci>rder (for platinum thnrmometers). 

Two complete Orubb'a controls (Aatrograph and Chronc^^nli i, 

UKiti^ ttio sidereal clock instead of an auxiliary pendulum. 
One cuntrui for menn time clock. 
Several small l«mp« on itislrunients. 
Two sounders for bnating seconds in dark rooma. 
Four call belJH. 
Two alarm bulls on Aatroifrapli. 

All eleotric connections are, in fact, worked frotu the A h 
lenninak cxcevl \.*h« ^lo\BV3 ft^Tttftt from the mean time cl— 



Apr. 1907. Electric Arrarufements of an Obsenfoioin/. 423 



.r 



Ss! 



X£ 



GQ 



D 

JO 



0:> 






IP 



< 
.0 



424 EUctric ArrangenunU of an OhaerveUory. LXTil 6l 

Eveu that is connected through A B to the multiple relay, bit 
theuce the aigoals have to be distribatod outside, and ik 
observatory is onlj supposed to make a contact once per boor,— 
each outside user supplying his own battery. "We outselvee tike 
one of these circuits and run it through various meteorologieil 
instruments, fire a gun, and control a public clock, but for Uiii 
purpose Ijeclanchd batteries are used. 



Perth Observatory, tt'e^em. AuMtrttlia. 



MONTHLY NOTICES 



OF THB 



ROYAL ASTRONOMICAL SOCIETY. 



Vql. LXVII. Mat io, 1907. No. 7 



H. F. Nbwall, Esq., M.A., F.R.S., President, in the Chair. 

The following candidates were proposed for election as Fellows 
of the Society, the names of the proposers from personal knowledge 
being appended : — 

Harold A. H. Christie, B.A., Rojal Observatory, Greenwich 

(proposed by Sir W. H. M, Cliristie) ; 
Bertram Francis Eardley Keeling, The Observatory, Helwan, 

near Cairo, Egypt (proposed by H, H. Turner) ; and 
Frederick Alexander Lindemann, Sidholme, Sidmouth, Devon 

(proposed by A. F. Lindemann). 

Sixty-nine presents were announced as liaving been received 
since the last meeting', including, amongst others : — 

Maurice Farman, Meaures d'l^toiles doubles, presented by the 
author; Harvard Observatory Annals, vol. 52, part i, Ei;lipses of 
Jupiter's satellites ; vol. 52, part 2, Second Catalogue of Viiriable 
Btars, presented by the Observatory; Heidelberg A.strophysical 
Observatory, Publications, vol. 2, Nos. 2-10, presentci! Ity the 
Observatory ; Meudon Observatory, Annals, vol. 3. piirt i, ])iesL;iitr(i 
by the Observatory; 20 cliarU nf the Aatiogriiphii: f'lnut uf tlie 
heavens, presented by the Royal Observatory, Greenwich. 



^■\ 



^'ott on Le Vcrrier's Tables <^f Haluriu 



426 



you on La Verrier'v TabU« of Satum. 
D.Sc. F.R.S. 




By A. 5f. W. Downing. 



My attention lias bften calle<l to the ra|iidly-iiicr«A«)ng discord- 
ance between the plftcca of Suturn dcriveri (nm I^ Vertier* tablet 
■nil tli'ise ilerive'l from tlie lAhlat of Hill, oa vhown by th« UtasI 
Availnlite dat«, i.t*. the Kphfrnnridfts for 1909. 

Tlitf followiog statement gives the conrectioui to ho VerrMt** 
geocentric |iliice9, near llie timu of opposition in 1901), m girwi in 
th* Ctmnaitmru-c de* Temps fur that year, deduced from thtix, 
compsrifion with the tiorreHponding places given in the iVd 
AUnanac : — 



Oot a 


ILA. 

I 

-I-09 


Dm. 
-6-8 


lO 


- no 


-6-9 


18 


-i-oS 


-6-8 



The comttponding oometiotii to tha halioeaotrio loDgil 
»re: — 

OoL 3 - 16*0 



It will b« roroemberod that M. Oatllot Itu pubiiihed ''Tal 
reetifi^ca du mouvemi'Ot dv Sttturne " in loniv xxlv. of tlt^ Annal* 
de VOfiMiTpatoimiie Ptiru, end 1L u nf ini'-mgt bi exhibit the resulting 
t»>rrectioiii to Le Verrter'a tielioocntric longitudes arconling to Hilli, 
mod according to Utillut, at conveoieat ejiocli*, as follows : — 



llPMlk 


Bin. 


0«11l9i 


1894 Mueb 6 


-3-8 


.'. 


1901 Jul 1 


- 3"$ 


- 4"9 


1909 OoL ID 


-15-9 


-i6*a 



The olwerred ntiniii cmrnction to Lo Verrittr'n junijitudM 
Ltnm, derircd fnini the (irrnnwich Obwrration* of 1900, is- 
whilst the ohwrr'Nl mtian correction to HiU'ii Iftngitndei, dmred 
from lb« <irc«nirlclt DbMrvntiuni of tho fotlowiriK ^ear (ihv 6nit 
yoar in which HiU'i tablo« wert* u»ed in the i\'aufirixl Attuttruu-), 
abimt half a second in the Karae senso ; itius d(*munatratiiig tbfl 
•uperior acrunoy nf IliU and tiailint at xh<* cnmmeiicemant of Uu 
eenturr. But it is important to note the rapid increase in tin 
diacurdnncn betw<<4>n Le Vcrricr and the otlicr two authuritiea linett 
thai timv. 



» 



Fay 1907. CamptUaiion 0/ Secular Perturhatioiis. 



427 



Computation of Setmiar Pa-turttationg. By R. T. A. Innea. 



It is well known that the Tjigrangian equationH for the rariation 

a planet'A phniaiits (tho plauet beiii^; considered of iiitiniteaiinal 

dimetir^ions) ure exact. It is in ttie iiitegratlun u£ tliese equations 

that difficulties arise. To avoid these difficulties several ftHsuriipiiona 

are mai!e, stich as that the ]>latiets can he ccmsidereii in pnirA (i.e. the 

roblaii) of three iKHliea) and du not reuct on each other ; that the 

lemcut^oti tlie righlr-hand hide of the U(|Uallunii iiru conmljint, iind 

iftt tlie |ifrturhativo fuiu-tioii can be developed in & roiivcrging 

snea. When we are concerned with the mutual perttirbfitionA of the 

ight major ;i1ani^t«, the above ossumptioud are sufficiently good ; the 

>rs intruducud by the tirst twu asKumptioiis are ijlLiiiiiialed later 

Ukiny into account the powers of the masses higher tlmn the 

the third assumption is noarly jiiHcifitid by the aiiinllnesH of 

le eccentricities and nLutnal inclinations of the eight major 

klanets. In cases uf difficulty, the Lu^rangian equations are 

^bauduiicd aurl the perlurbatious foutid by other processes; ttiua 

Hll found tlmt the Lagiitii-iiari mothod an used hy J^ Verrier for 

le thenry of the motion of Jupiter and Satum was insuffioierit, so 

lat in his theory be adopted the processes developed hy Hansen. 

Giiii:-«) showed thiit the secular [lurl of the purlurhatit'lis (to tlie 
Srst power of the luasses) could be found without using a dtvelop- 
lent id thf pertiirbative function. Tlie rationale of Gauss's niiflhod 
as follows: — Let us imagine that the perturbative function is 
developed in a series as followit, 

Pfl " Pi + i**»*" M + P< cos M + ?^ sin sM + etc. 

rherc the coeffioienta P contain, be«idos certain quantities 
•pendirig on the eleuienta of tlie disturbed plunet, the elementa 
id position of the disturbing body. MitUiplying each sido by 
and integrating around the circumference gives 



^^fp/M.P, 



?hen writing l*i=Pi+Pn "'^ Mj+p^cos Mj + etc., where the co- 
^icients p depend only on the etemeut^ of both planets and do not 
jntain tlie time explicitly, a second integration gives 



4-^i7/>»'"f''*^'=''' 



. is on the quantity />, that ilia secular perturbations depend. In 
ae general case it is impossible to Hnd this quantity by algebraical 
ci»aiisiona. Gauaa proved that one of tbese mlei^ta.\\':)X\R tvi\i.\^ \i«i 



438 



Mr S. T. A. Inws, 



LXVIL 7. 




"7 



reduced to elliptic iategraU ; the ncond has to be a mfldmnioAl 
integratiuii. Gauss, us in n-ell-knovvu, ^'nvo n gaom«lrictiI title to 
hiB [Mpt^r and did not prefxiro liix funnulje for uurnvhrnt applicntio 
Bour and othpr? have givfn further geometrical inlorpretatioos 
Oau&j's formoliQ, which, interesting oi they ar«, call lor no aueo 
here. 

Since Dr. G. W. Hill published his first pa|>er on G* 
Metho<) of Computing the Secular iVrturhaiions uf the 1*1 
(Astron. Papum i(re)»ared for tlie use of the Amoncan Ei)heQiena, 
iSSx ; Collected Wurkfl, T. ii., 1906) many numerical applicatiaas 
of this motliod have beon made. Hill did uvt leave tht* method in 
Bnal ahape. for no nooiier had he finiihe<l hia paper than h* pio- 
ceeded to give a auhatautiul mollification in an addeudnm hj 
making uae uf Gauns'a arilhmoticogi-uitictricBl ni^nn. Both o| 
Hill'a solutions require extonsire talileo uf the elliptic integrals 
their eaiy application, llill pruvirle<l the.ic tallies for hie 
Bolutinn, and Callaadrean aiid the writer did the «ume fur Ilil 
aecond method. PreTiou»ly to Hill'a work there had b«an 
little use made of Guuui'a method. We learn from liode'a A*fro- 
noi»i$ffiet Jafti-ftucfi, 1819, p. 239, that before Qaiua bad actually 
published hift memoir, Xic-olai had computed the m^<\ var. of (h« 
elements of the Earth's orbit by this method, hut no tl«<tail« of the 
work were given. Tiie late Professor J. C. Ailauis applied the 
iaetbo<l to thn pertarbntion of tliu nrhii nf the November Mei 
(wnM. N., 1S67, Apl. ; Collected Wurks, T. ii. pp. 194-J00). It 
well known that the methoil aa expoanded by Uanu recjuiroa 
■olutiiin o( a cubic equation, but Adams avoida the rabic hy negl 
ing a i)ortiou of the terms factored by the square of the occi-ntricit, 
of the disturbing body, and so mluctei the e<jUAtioa to a (|iiadrfe 
This i« no dtiubt the modification which Adams stated greAtl; 
facilitates t